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anderson_darling_cdf


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 -- Function File: P = anderson_darling_cdf (A, N)

     Return the CDF for the given Anderson-Darling coefficient A
     computed from N values sampled from a distribution.  For a vector
     of random variables X of length N, compute the CDF of the values
     from the distribution from which they are drawn.  You can uses
     these values to compute A as follows:

          A = -N - sum( (2*i-1) .* (log(X) + log(1 - X(N:-1:1,:))) )/N;

     From the value A, 'anderson_darling_cdf' returns the probability
     that A could be returned from a set of samples.

     The algorithm given in [1] claims to be an approximation for the
     Anderson-Darling CDF accurate to 6 decimal points.

     Demonstrate using:

          n = 300; reps = 10000;
          z = randn(n, reps);
          x = sort ((1 + erf (z/sqrt (2)))/2);
          i = [1:n]' * ones (1, size (x, 2));
          A = -n - sum ((2*i-1) .* (log (x) + log (1 - x (n:-1:1, :))))/n;
          p = anderson_darling_cdf (A, n);
          hist (100 * p, [1:100] - 0.5);

     You will see that the histogram is basically flat, which is to say
     that the probabilities returned by the Anderson-Darling CDF are
     distributed uniformly.

     You can easily determine the extreme values of P:

          [junk, idx] = sort (p);

     The histograms of various P aren't very informative:

          histfit (z (:, idx (1)), linspace (-3, 3, 15));
          histfit (z (:, idx (end/2)), linspace (-3, 3, 15));
          histfit (z (:, idx (end)), linspace (-3, 3, 15));

     More telling is the qqplot:

          qqplot (z (:, idx (1))); hold on; plot ([-3, 3], [-3, 3], ';;'); hold off;
          qqplot (z (:, idx (end/2))); hold on; plot ([-3, 3], [-3, 3], ';;'); hold off;
          qqplot (z (:, idx (end))); hold on; plot ([-3, 3], [-3, 3], ';;'); hold off;

     Try a similarly analysis for Z uniform:

          z = rand (n, reps); x = sort(z);

     and for Z exponential:

          z = rande (n, reps); x = sort (1 - exp (-z));

     [1] Marsaglia, G; Marsaglia JCW; (2004) "Evaluating the Anderson
     Darling distribution", Journal of Statistical Software, 9(2).

     See also: anderson_darling_test.


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Return the CDF for the given Anderson-Darling coefficient A computed
from N v...



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bbscdf


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 -- bbscdf (X, SHAPE, SCALE, LOCATION)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Birnbaum-Saunders distribution with parameters
     LOCATION, SCALE and SHAPE.


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For each element of X, compute the cumulative distribution function
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bbsinv


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 -- bbsinv (X, SHAPE, SCALE, LOCATION)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the Birnbaum-Saunders distribution with parameters
     LOCATION, SCALE, and SHAPE.


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For each element of X, compute the quantile (the inverse of the CDF) at
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bbspdf


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 -- bbspdf (X, SHAPE, SCALE, LOCATION)
     For each element of X, compute the probability density function
     (PDF) at X of the Birnbaum-Saunders distribution with parameters
     LOCATION, SCALE and SHAPE.


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For each element of X, compute the probability density function (PDF) at
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bbsrnd


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 -- bbsrnd (SHAPE, SCALE, LOCATION)
 -- bbsrnd (SHAPE, SCALE, LOCATION, R)
 -- bbsrnd (SHAPE, SCALE, LOCATION, R, C, ...)
 -- bbsrnd (SHAPE, SCALE, LOCATION, [SZ])
     Return a matrix of random samples from the Birnbaum-Saunders
     distribution with parameters LOCATION, SCALE and SHAPE.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of LOCATION, SCALE and SHAPE.


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Return a matrix of random samples from the Birnbaum-Saunders
distribution wit...



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betacdf


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 -- betacdf (X, A, B)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Beta distribution with parameters A and B.


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For each element of X, compute the cumulative distribution function
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betainv


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 -- betainv (X, A, B)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the Beta distribution with parameters A and B.


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For each element of X, compute the quantile (the inverse of the CDF) at
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betapdf


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 -- betapdf (X, A, B)
     For each element of X, compute the probability density function
     (PDF) at X of the Beta distribution with parameters A and B.


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For each element of X, compute the probability density function (PDF) at
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betarnd


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 -- betarnd (A, B)
 -- betarnd (A, B, R)
 -- betarnd (A, B, R, C, ...)
 -- betarnd (A, B, [SZ])
     Return a matrix of random samples from the Beta distribution with
     parameters A and B.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of A and B.


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Return a matrix of random samples from the Beta distribution with
parameters ...



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binocdf


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 -- Function File: binocdf (X, N, P)
 -- Function File: binocdf (X, N, P, 'upper')

     For each element of X, compute the cumulative distribution function
     (CDF) at X of the binomial distribution with parameters N and P,
     where N is the number of trials and P is the probability of
     success.

     binocdf (X, N, P, 'upper') computes the complement of the
     cumulative distribution function.


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For each element of X, compute the cumulative distribution function
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binoinv


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 -- binoinv (X, N, P)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the binomial distribution with parameters N and P,
     where N is the number of trials and P is the probability of
     success.


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For each element of X, compute the quantile (the inverse of the CDF) at
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binopdf


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 -- Z = binopdf (X, N, P)
     For each element of X, compute the probability density function
     (PDF) at X of the binomial distribution with parameters N and P,
     where N is the number of trials and P is the probability of
     success.

     The inputs X, N, and P can be scalars or arrays.  If more than one
     is an array, they must be of equal size.  The output Z will have
     the same size as the array inputs.

     Matlab incompatibility: Octave's 'binopdf' returns NaN for complex
     input values.


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binornd


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 -- binornd (N, P)
 -- binornd (N, P, R)
 -- binornd (N, P, R, C, ...)
 -- binornd (N, P, [SZ])
     Return a matrix of random samples from the binomial distribution
     with parameters N and P, where N is the number of trials and P is
     the probability of success.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of N and P.


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Return a matrix of random samples from the binomial distribution with
paramet...



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burrcdf


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 -- burrcdf (X, C, K)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Burr distribution with scale parameter ALPHA and
     shape parameters C and K.


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For each element of X, compute the cumulative distribution function
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burrinv


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 -- burrinv (X, ALPHA, C, K)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the Burr distribution with scale parameter ALPHA and
     shape parameters C and K.


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For each element of X, compute the quantile (the inverse of the CDF) at
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burrpdf


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 -- burrpdf (X, ALPHA, C, K)
     For each element of X, compute the probability density function
     (PDF) at X of the Burr distribution with scale parameter ALPHA and
     shape parameters C and K.


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burrrnd


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 -- burrrnd (ALPHA, C, K)
 -- burrrnd (ALPHA, C, K, R)
 -- burrrnd (ALPHA, C, K, R, C, ...)
 -- burrrnd (ALPHA, C, K, [SZ])
     Return a matrix of random samples from the generalized Pareto
     distribution with scale parameter ALPHA and shape parameters C and
     K.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of ALPHA, C and K.


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Return a matrix of random samples from the generalized Pareto
distribution wi...



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bvncdf


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 -- Function File: P = bvncdf (X, MU, SIGMA)
 -- Function File: P = bvncdf (X, [], SIGMA)

     Bivariate normal cumulative distribution function.

     'P = bvncdf (X, MU, SIGMA)' will compute the bivariate normal
     cumulative distribution function of X given a mean MU, which must
     be a scalar, and a 2x2 SIGMA covariance matrix, which must be
     positive definite.


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Bivariate normal cumulative distribution function.



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cauchy_cdf


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 -- cauchy_cdf (X)
 -- cauchy_cdf (X, LOCATION, SCALE)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Cauchy distribution with location parameter
     LOCATION and scale parameter SCALE.

     Default values are LOCATION = 0, SCALE = 1.


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For each element of X, compute the cumulative distribution function
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cauchy_inv


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 -- cauchy_inv (X)
 -- cauchy_inv (X, LOCATION, SCALE)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the Cauchy distribution with location parameter
     LOCATION and scale parameter SCALE.

     Default values are LOCATION = 0, SCALE = 1.


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cauchy_pdf


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 -- cauchy_pdf (X)
 -- cauchy_pdf (X, LOCATION, SCALE)
     For each element of X, compute the probability density function
     (PDF) at X of the Cauchy distribution with location parameter
     LOCATION and scale parameter SCALE > 0.

     Default values are LOCATION = 0, SCALE = 1.


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For each element of X, compute the probability density function (PDF) at
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cauchy_rnd


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 -- cauchy_rnd (LOCATION, SCALE)
 -- cauchy_rnd (LOCATION, SCALE, R)
 -- cauchy_rnd (LOCATION, SCALE, R, C, ...)
 -- cauchy_rnd (LOCATION, SCALE, [SZ])
     Return a matrix of random samples from the Cauchy distribution with
     parameters LOCATION and SCALE.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of LOCATION and SCALE.


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Return a matrix of random samples from the Cauchy distribution with
parameter...



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chi2cdf


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 -- Function File: P = tcdf (X, V)
 -- Function File: P = tcdf (X, V, "upper")

     Chi-square cumulative distribution function.

     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Chi-Squared distribution with V degrees of
     freedom.  The chi-square density function with V degrees of freedom
     is the same as a gamma density function with parameters V/2 and 2.

     The size of P is the common size of X and V.  A scalar input
     functions as a constant matrix of the same size as the other input.

     'P = fcdf (X, V, "upper")' computes the upper tail probability of
     the Chi-Squared distribution with V degrees of freedom at the
     values in X.

     See also: chi2inv, chi2pdf, chi2rnd, chi2stat.


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Chi-square cumulative distribution function.



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chi2inv


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 -- chi2inv (X, N)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the chi-square distribution with N degrees of freedom.


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For each element of X, compute the quantile (the inverse of the CDF) at
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chi2pdf


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 -- chi2pdf (X, N)
     For each element of X, compute the probability density function
     (PDF) at X of the chi-square distribution with N degrees of
     freedom.


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For each element of X, compute the probability density function (PDF) at
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chi2rnd


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 -- chi2rnd (N)
 -- chi2rnd (N, R)
 -- chi2rnd (N, R, C, ...)
 -- chi2rnd (N, [SZ])
     Return a matrix of random samples from the chi-square distribution
     with N degrees of freedom.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the size
     of N.


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Return a matrix of random samples from the chi-square distribution with
N deg...



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copulacdf


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 -- Function File: P = copulacdf (FAMILY, X, THETA)
 -- Function File: copulacdf ('t', X, THETA, NU)
     Compute the cumulative distribution function of a copula family.

     Arguments
     ---------

        * FAMILY is the copula family name.  Currently, FAMILY can be
          ''Gaussian'' for the Gaussian family, ''t'' for the Student's
          t family, ''Clayton'' for the Clayton family, ''Gumbel'' for
          the Gumbel-Hougaard family, ''Frank'' for the Frank family,
          ''AMH'' for the Ali-Mikhail-Haq family, or ''FGM'' for the
          Farlie-Gumbel-Morgenstern family.

        * X is the support where each row corresponds to an observation.

        * THETA is the parameter of the copula.  For the Gaussian and
          Student's t copula, THETA must be a correlation matrix.  For
          bivariate copulas THETA can also be a correlation coefficient.
          For the Clayton family, the Gumbel-Hougaard family, the Frank
          family, and the Ali-Mikhail-Haq family, THETA must be a vector
          with the same number of elements as observations in X or be
          scalar.  For the Farlie-Gumbel-Morgenstern family, THETA must
          be a matrix of coefficients for the Farlie-Gumbel-Morgenstern
          polynomial where each row corresponds to one set of
          coefficients for an observation in X.  A single row is
          expanded.  The coefficients are in binary order.

        * NU is the degrees of freedom for the Student's t family.  NU
          must be a vector with the same number of elements as
          observations in X or be scalar.

     Return values
     -------------

        * P is the cumulative distribution of the copula at each row of
          X and corresponding parameter THETA.

     Examples
     --------

          x = [0.2:0.2:0.6; 0.2:0.2:0.6];
          theta = [1; 2];
          p = copulacdf ("Clayton", x, theta)

          x = [0.2:0.2:0.6; 0.2:0.1:0.4];
          theta = [0.2, 0.1, 0.1, 0.05];
          p = copulacdf ("FGM", x, theta)

     References
     ----------

       1. Roger B. Nelsen.  'An Introduction to Copulas'.  Springer, New
          York, second edition, 2006.


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Compute the cumulative distribution function of a copula family.



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copulapdf


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 -- Function File: P = copulapdf (FAMILY, X, THETA)
     Compute the probability density function of a copula family.

     Arguments
     ---------

        * FAMILY is the copula family name.  Currently, FAMILY can be
          ''Clayton'' for the Clayton family, ''Gumbel'' for the
          Gumbel-Hougaard family, ''Frank'' for the Frank family, or
          ''AMH'' for the Ali-Mikhail-Haq family.

        * X is the support where each row corresponds to an observation.

        * THETA is the parameter of the copula.  The elements of THETA
          must be greater than or equal to '-1' for the Clayton family,
          greater than or equal to '1' for the Gumbel-Hougaard family,
          arbitrary for the Frank family, and greater than or equal to
          '-1' and lower than '1' for the Ali-Mikhail-Haq family.
          Moreover, THETA must be non-negative for dimensions greater
          than '2'.  THETA must be a column vector with the same number
          of rows as X or be scalar.

     Return values
     -------------

        * P is the probability density of the copula at each row of X
          and corresponding parameter THETA.

     Examples
     --------

          x = [0.2:0.2:0.6; 0.2:0.2:0.6];
          theta = [1; 2];
          p = copulapdf ("Clayton", x, theta)

          p = copulapdf ("Gumbel", x, 2)

     References
     ----------

       1. Roger B. Nelsen.  'An Introduction to Copulas'.  Springer, New
          York, second edition, 2006.


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Compute the probability density function of a copula family.



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copularnd


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 -- Function File: X = copularnd (FAMILY, THETA, N)
 -- Function File: copularnd (FAMILY, THETA, N, D)
 -- Function File: copularnd ('t', THETA, NU, N)
     Generate random samples from a copula family.

     Arguments
     ---------

        * FAMILY is the copula family name.  Currently, FAMILY can be
          ''Gaussian'' for the Gaussian family, ''t'' for the Student's
          t family, or ''Clayton'' for the Clayton family.

        * THETA is the parameter of the copula.  For the Gaussian and
          Student's t copula, THETA must be a correlation matrix.  For
          bivariate copulas THETA can also be a correlation coefficient.
          For the Clayton family, THETA must be a vector with the same
          number of elements as samples to be generated or be scalar.

        * NU is the degrees of freedom for the Student's t family.  NU
          must be a vector with the same number of elements as samples
          to be generated or be scalar.

        * N is the number of rows of the matrix to be generated.  N must
          be a non-negative integer and corresponds to the number of
          samples to be generated.

        * D is the number of columns of the matrix to be generated.  D
          must be a positive integer and corresponds to the dimension of
          the copula.

     Return values
     -------------

        * X is a matrix of random samples from the copula with N samples
          of distribution dimension D.

     Examples
     --------

          theta = 0.5;
          x = copularnd ("Gaussian", theta);

          theta = 0.5;
          nu = 2;
          x = copularnd ("t", theta, nu);

          theta = 0.5;
          n = 2;
          x = copularnd ("Clayton", theta, n);

     References
     ----------

       1. Roger B. Nelsen.  'An Introduction to Copulas'.  Springer, New
          York, second edition, 2006.


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Generate random samples from a copula family.



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evcdf


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 -- Function File: P = evcdf (X)
 -- Function File: P = evcdf (X, MU)
 -- Function File: P = evcdf (X, MU, SIGMA)
 -- Function File: P = evcdf (..., "upper")
 -- Function File: [P, PLO, PUP] = evcdf (X, MU, SIGMA, PCOV)
 -- Function File: [P, PLO, PUP] = evcdf (X, MU, SIGMA, PCOV, ALPHA)
 -- Function File: [P, PLO, PUP] = evcdf (..., "upper")

     Extreme value cumulative distribution function (cdf).

     For each element of X, compute the cumulative distribution function
     (CDF) of the type 1 extreme values CDF at X of the normal
     distribution with location parameter MU and scale parameter SIGMA.
     The size of P is the common size of X, MU and SIGMA.  A scalar
     input functions as a constant matrix of the same size as the other
     inputs.

     Default values are MU = 0, SIGMA = 1.

     When called with three output arguments, '[P, PLO, PUP]' it
     computes the confidence bounds for P when the input parameters MU
     and SIGMA are estimates.  In such case, PCOV, a 2-by-2 matrix
     containing the covariance matrix of the estimated parameters, is
     necessary.  Optionally, ALPHA has a default value of 0.05, and
     specifies 100 * (1 - ALPHA)% confidence bounds.  PLO and PUP are
     arrays of the same size as P containing the lower and upper
     confidence bounds.

     The type 1 extreme value distribution is also known as the Gumbel
     distribution.  The version used here is suitable for modeling
     minima; the mirror image of this distribution can be used to model
     maxima by negating X.  If Y has a Weibull distribution, then 'X =
     log (Y)' has the type 1 extreme value distribution.

     '[...] = evcdf (..., "upper")' computes the upper tail probability
     of the extreme value distribution.

     See also: evinv, evpdf, evrnd, evfit, evlike, evstat.


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Extreme value cumulative distribution function (cdf).



# name: <cell-element>
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evinv


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 -- Function File: X = evinv (P)
 -- Function File: X = evcdf (P, MU)
 -- Function File: X = evinv (P, MU, SIGMA)
 -- Function File: [X, XLO, XUP] = evinv (X, MU, SIGMA, PCOV)
 -- Function File: [X, XLO, XUP] = evinv (X, MU, SIGMA, PCOV, ALPHA)

     Inverse of the extreme value cumulative distribution function
     (cdf).

     For each element of P, compute the inverse cdf for a type 1 extreme
     value distribution with location parameter MU and scale parameter
     SIGMA.  The size of X is the common size of P, MU and SIGMA.  A
     scalar input functions as a constant matrix of the same size as the
     other inputs.

     Default values are MU = 0, SIGMA = 1.

     When called with three output arguments, '[X, XLO, XUP]' it
     computes the confidence bounds for X when the input parameters MU
     and SIGMA are estimates.  In such case, PCOV, a 2-by-2 matrix
     containing the covariance matrix of the estimated parameters, is
     necessary.  Optionally, ALPHA has a default value of 0.05, and
     specifies 100 * (1 - ALPHA)% confidence bounds.  XLO and XUP are
     arrays of the same size as X containing the lower and upper
     confidence bounds.

     The type 1 extreme value distribution is also known as the Gumbel
     distribution.  The version used here is suitable for modeling
     minima; the mirror image of this distribution can be used to model
     maxima by negating X.  If Y has a Weibull distribution, then 'X =
     log (Y)' has the type 1 extreme value distribution.

     See also: evcdf, evpdf, evrnd, evfit, evlike, evstat.


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Inverse of the extreme value cumulative distribution function (cdf).



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evpdf


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 -- Function File: Y = evpdf (X)
 -- Function File: Y = evpdf (X, MU)
 -- Function File: Y = evpdf (X, MU, SIGMA)

     Extreme value probability density function (pdf).

     'Y = evpdf (X, MU, SIGMA)' returns the pdf of the type 1 extreme
     value distribution with location parameter MU and scale parameter
     SIGMA.  The size of X is the common size of P, MU and SIGMA.  A
     scalar input functions as a constant matrix of the same size as the
     other inputs.

     Default values are MU = 0, SIGMA = 1.

     The type 1 extreme value distribution is also known as the Gumbel
     distribution.  The version used here is suitable for modeling
     minima; the mirror image of this distribution can be used to model
     maxima by negating X.  If Y has a Weibull distribution, then 'X =
     log (Y)' has the type 1 extreme value distribution.

     See also: evcdf, evinv, evrnd, evfit, evlike, evstat.


# name: <cell-element>
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Extreme value probability density function (pdf).



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evrnd


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 -- Function File: R = evrnd (MU, SIGMA)
 -- Function File: R = evrnd (MU, SIGMA, M, N, ...)
 -- Function File: R = evrnd (MU, SIGMA, [M, N, ...])

     Random arrays from the extreme value distribution.

     'R = evrnd (MU, SIGMA)' returns an array of random numbers chosen
     from the type 1 extreme value distribution with location parameter
     MU and scale parameter SIGMA.  The size of R is the common size of
     MU and SIGMA.  A scalar input functions as a constant matrix of the
     same size as the other inputs.

     'R = evrnd (MU, SIGMA, M, N, ...)' or 'R = evrnd (MU, SIGMA, [M, N,
     ...])' returns an M-by-N-by-...  array.

     The type 1 extreme value distribution is also known as the Gumbel
     distribution.  The version used here is suitable for modeling
     minima; the mirror image of this distribution can be used to model
     maxima by negating X.  If Y has a Weibull distribution, then 'X =
     log (Y)' has the type 1 extreme value distribution.

     See also: evcdf, evinv, evpdf, evfit, evlike, evstat.


# name: <cell-element>
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Random arrays from the extreme value distribution.



# name: <cell-element>
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expcdf


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 -- expcdf (X, LAMBDA)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the exponential distribution with mean LAMBDA.

     The arguments can be of common size or scalars.


# name: <cell-element>
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# length: 80
For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
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# length: 6
expinv


# name: <cell-element>
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# length: 156
 -- expinv (X, LAMBDA)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the exponential distribution with mean LAMBDA.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
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# elements: 1
# length: 6
exppdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 157
 -- exppdf (X, LAMBDA)
     For each element of X, compute the probability density function
     (PDF) at X of the exponential distribution with mean LAMBDA.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
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exprnd


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 -- exprnd (LAMBDA)
 -- exprnd (LAMBDA, R)
 -- exprnd (LAMBDA, R, C, ...)
 -- exprnd (LAMBDA, [SZ])
     Return a matrix of random samples from the exponential distribution
     with mean LAMBDA.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the size
     of LAMBDA.


# name: <cell-element>
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Return a matrix of random samples from the exponential distribution with
mean...



# name: <cell-element>
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# length: 4
fcdf


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 -- Function File: P = tcdf (X, V1, V2)
 -- Function File: P = tcdf (X, V1, V2, "upper")

     F cumulative distribution function.

     For each element of X, compute the cumulative distribution function
     (CDF) at X of the F distribution with V1 and V2 degrees of freedom.

     The size of P is the common size of X, V1, and V2.  A scalar input
     functions as a constant matrix of the same size as the other
     inputs.

     'P = fcdf (X, V1, V2, "upper")' computes the upper tail probability
     of the F distribution with V1 and V2 degrees of freedom at the
     values in X.

     See also: finv, fpdf, frnd, fstat.


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F cumulative distribution function.



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finv


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# length: 157
 -- finv (X, M, N)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the F distribution with M and N degrees of freedom.


# name: <cell-element>
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For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
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# length: 4
fpdf


# name: <cell-element>
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# length: 158
 -- fpdf (X, M, N)
     For each element of X, compute the probability density function
     (PDF) at X of the F distribution with M and N degrees of freedom.


# name: <cell-element>
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# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
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frnd


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 -- frnd (M, N)
 -- frnd (M, N, R)
 -- frnd (M, N, R, C, ...)
 -- frnd (M, N, [SZ])
     Return a matrix of random samples from the F distribution with M
     and N degrees of freedom.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of M and N.


# name: <cell-element>
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# length: 80
Return a matrix of random samples from the F distribution with M and N
degree...



# name: <cell-element>
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# elements: 1
# length: 6
gamcdf


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 -- Function File: P = gamcdf (X, A)
 -- Function File: P = gamcdf (X, A, B)
 -- Function File: P = gamcdf (..., "upper")
 -- Function File: [P, PLO, PUP] = evcdf (X, A, B, PCOV)
 -- Function File: [P, PLO, PUP] = evcdf (X, A, B, PCOV, ALPHA)
 -- Function File: [P, PLO, PUP] = evcdf (..., "upper")

     Gamma cumulative distribution function.

     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Gamma distribution with shape parameter A and
     scale B.  When called with only one parameter, then B defaults to
     1.  The size of P is the common size of X, A, and B.  A scalar
     input functions as a constant matrix of the same size as the other
     inputs.

     When called with three output arguments, '[P, PLO, PUP]' it
     computes the confidence bounds for P when the input parameters A
     and B are estimates.  In such case, PCOV, a 2-by-2 matrix
     containing the covariance matrix of the estimated parameters, is
     necessary.  Optionally, ALPHA has a default value of 0.05, and
     specifies 100 * (1 - ALPHA)% confidence bounds.  PLO and PUP are
     arrays of the same size as P containing the lower and upper
     confidence bounds.

     '[...] = gamcdf (..., "upper")' computes the upper tail probability
     of the gamma distribution.

     See also: gaminv, gampdf, gamrnd, gamfit, gamlike, gamstat.


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Gamma cumulative distribution function.



# name: <cell-element>
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gaminv


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# length: 171
 -- gaminv (X, A, B)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the Gamma distribution with shape parameter A and
     scale B.


# name: <cell-element>
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For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
gampdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
 -- gampdf (X, A, B)
     For each element of X, return the probability density function
     (PDF) at X of the Gamma distribution with shape parameter A and
     scale B.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, return the probability density function (PDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
gamrnd


# name: <cell-element>
# type: sq_string
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# length: 664
 -- gamrnd (A, B)
 -- gamrnd (A, B, R)
 -- gamrnd (A, B, R, C, ...)
 -- gamrnd (A, B, [SZ])
     Return a matrix of random samples from the Gamma distribution with
     shape parameter A and scale B.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of A and B.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return a matrix of random samples from the Gamma distribution with shape
para...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
geocdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 292
 -- geocdf (X, P)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the geometric distribution with parameter P.

     The geometric distribution models the number of failures (X) of a
     Bernoulli trial with probability P before the first success.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
# type: sq_string
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# length: 6
geoinv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
 -- geoinv (X, P)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the geometric distribution with parameter P.

     The geometric distribution models the number of failures (X) of a
     Bernoulli trial with probability P before the first success.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
geopdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 288
 -- geopdf (X, P)
     For each element of X, compute the probability density function
     (PDF) at X of the geometric distribution with parameter P.

     The geometric distribution models the number of failures (X) of a
     Bernoulli trial with probability P before the first success.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
geornd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 763
 -- geornd (P)
 -- geornd (P, R)
 -- geornd (P, R, C, ...)
 -- geornd (P, [SZ])
     Return a matrix of random samples from the geometric distribution
     with parameter P.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the size
     of P.

     The geometric distribution models the number of failures (X) of a
     Bernoulli trial with probability P before the first success.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return a matrix of random samples from the geometric distribution with
parame...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
gevcdf


# name: <cell-element>
# type: sq_string
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# length: 1260
 -- Function File: P = gevcdf (X, K, SIGMA, MU)
     Compute the cumulative distribution function of the generalized
     extreme value (GEV) distribution.

     Arguments
     ---------

        * X is the support.

        * K is the shape parameter of the GEV distribution.  (Also
          denoted gamma or xi.)
        * SIGMA is the scale parameter of the GEV distribution.  The
          elements of SIGMA must be positive.
        * MU is the location parameter of the GEV distribution.
     The inputs must be of common size, or some of them must be scalar.

     Return values
     -------------

        * P is the cumulative distribution of the GEV distribution at
          each element of X and corresponding parameter values.

     Examples
     --------

          x = 0:0.5:2.5;
          sigma = 1:6;
          k = 1;
          mu = 0;
          y = gevcdf (x, k, sigma, mu)

          y = gevcdf (x, k, 0.5, mu)

     References
     ----------

       1. Rolf-Dieter Reiss and Michael Thomas.  'Statistical Analysis
          of Extreme Values with Applications to Insurance, Finance,
          Hydrology and Other Fields'.  Chapter 1, pages 16-17,
          Springer, 2007.

     See also: gevfit, gevinv, gevlike, gevpdf, gevrnd, gevstat.


# name: <cell-element>
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Compute the cumulative distribution function of the generalized extreme
value...



# name: <cell-element>
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# length: 6
gevinv


# name: <cell-element>
# type: sq_string
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# length: 1214
 -- Function File: X = gevinv (P, K, SIGMA, MU)
     Compute a desired quantile (inverse CDF) of the generalized extreme
     value (GEV) distribution.

     Arguments
     ---------

        * P is the desired quantile of the GEV distribution.  (Between 0
          and 1.)
        * K is the shape parameter of the GEV distribution.  (Also
          denoted gamma or xi.)
        * SIGMA is the scale parameter of the GEV distribution.  The
          elements of SIGMA must be positive.
        * MU is the location parameter of the GEV distribution.
     The inputs must be of common size, or some of them must be scalar.

     Return values
     -------------

        * X is the value corresponding to each quantile of the GEV
          distribution

     References
     ----------

       1. Rolf-Dieter Reiss and Michael Thomas.  'Statistical Analysis
          of Extreme Values with Applications to Insurance, Finance,
          Hydrology and Other Fields'.  Chapter 1, pages 16-17,
          Springer, 2007.
       2. J. R. M. Hosking (2012).  'L-moments'.  R package, version
          1.6.  URL: http://CRAN.R-project.org/package=lmom.

     See also: gevcdf, gevfit, gevlike, gevpdf, gevrnd, gevstat.


# name: <cell-element>
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Compute a desired quantile (inverse CDF) of the generalized extreme
value (GE...



# name: <cell-element>
# type: sq_string
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# length: 6
gevpdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1252
 -- Function File: Y = gevpdf (X, K, SIGMA, MU)
     Compute the probability density function of the generalized extreme
     value (GEV) distribution.

     Arguments
     ---------

        * X is the support.

        * K is the shape parameter of the GEV distribution.  (Also
          denoted gamma or xi.)
        * SIGMA is the scale parameter of the GEV distribution.  The
          elements of SIGMA must be positive.
        * MU is the location parameter of the GEV distribution.
     The inputs must be of common size, or some of them must be scalar.

     Return values
     -------------

        * Y is the probability density of the GEV distribution at each
          element of X and corresponding parameter values.

     Examples
     --------

          x = 0:0.5:2.5;
          sigma = 1:6;
          k = 1;
          mu = 0;
          y = gevpdf (x, k, sigma, mu)

          y = gevpdf (x, k, 0.5, mu)

     References
     ----------

       1. Rolf-Dieter Reiss and Michael Thomas.  'Statistical Analysis
          of Extreme Values with Applications to Insurance, Finance,
          Hydrology and Other Fields'.  Chapter 1, pages 16-17,
          Springer, 2007.

     See also: gevcdf, gevfit, gevinv, gevlike, gevrnd, gevstat.


# name: <cell-element>
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Compute the probability density function of the generalized extreme
value (GE...



# name: <cell-element>
# type: sq_string
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# length: 6
gevrnd


# name: <cell-element>
# type: sq_string
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# length: 857
 -- Function File: gevrnd (K, SIGMA, MU)
 -- Function File: gevrnd (K, SIGMA, MU, R)
 -- Function File: gevrnd (K, SIGMA, MU, R, C, ...)
 -- Function File: gevrnd (K, SIGMA, MU, [SZ])
     Return a matrix of random samples from the generalized extreme
     value (GEV) distribution with parameters K, SIGMA, MU.

     When called with a single size argument, returns a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector SZ
     of dimensions.

     If no size arguments are given, then the result matrix is the
     common size of the input parameters.

     See also: gevcdf, gevfit, gevinv, gevlike, gevpdf, gevstat.


# name: <cell-element>
# type: sq_string
# elements: 1
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Return a matrix of random samples from the generalized extreme value
(GEV) di...



# name: <cell-element>
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# elements: 1
# length: 5
gpcdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1400
 -- Function File: P = gpcdf (X)
 -- Function File: P = gpcdf (X, SHAPE)
 -- Function File: P = gpcdf (X, SHAPE, SCALE)
 -- Function File: P = gpcdf (X, SHAPE, SCALE, LOCATION)
 -- Function File: P = gpcdf (..., "upper")

     Generalized Pareto cumulative distribution function (cdf).

     Compute the cumulative distribution function (CDF) at X of the
     generalized Pareto distribution with parameters LOCATION, SCALE,
     and SHAPE.  The size of P is the common size of the input
     arguments.  A scalar input functions as a constant matrix of the
     same size as the other inputs.

     Default values for SHAPE, SCALE, and LOCATION are 0, 1, and 0,
     respectively.

     When 'SHAPE = 0' and 'LOCATION = 0', the Generalized Pareto CDF is
     equivalent to the exponential distribution.  When 'SHAPE > 0' and
     'LOCATION = SHAPE / SHAPE' the Generalized Pareto is equivalent to
     the Pareto distribution.  The mean of the Generalized Pareto is not
     finite when 'SHAPE >= 1' and the variance is not finite when 'SHAPE
     >= 1/2'.  When 'SHAPE >= 0', the Generalized Pareto has positive
     density for 'X > LOCATION', or, when 'LOCATION < 0',for '0 <= (X -
     LOCATION) / SCALE <= -1 / SHAPE'.

     '[...] = gpcdf(..., "upper")' returns the upper tail probability of
     the generalized Pareto distribution.

     See also: gpinv, gppdf, gprnd, gpfit, gplike, gpstat.


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Generalized Pareto cumulative distribution function (cdf).



# name: <cell-element>
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gpinv


# name: <cell-element>
# type: sq_string
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# length: 209
 -- gpinv (X, SHAPE, SCALE, LOCATION)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the generalized Pareto distribution with parameters
     LOCATION, SCALE, and SHAPE.


# name: <cell-element>
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# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
gppdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 187
 -- gppdf (X, SHAPE, SCALE, LOCATION)
     Compute the probability density function (PDF) at X of the
     generalized Pareto distribution with parameters LOCATION, SCALE,
     and SHAPE.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the probability density function (PDF) at X of the generalized
Pareto...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
gprnd


# name: <cell-element>
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 -- gprnd (SHAPE, SCALE, LOCATION)
 -- gprnd (SHAPE, SCALE, LOCATION, R)
 -- gprnd (SHAPE, SCALE, LOCATION, R, C, ...)
 -- gprnd (SHAPE, SCALE, LOCATION, [SZ])
     Return a matrix of random samples from the generalized Pareto
     distribution with parameters LOCATION, SCALE and SHAPE.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of LOCATION, SCALE and SHAPE.


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Return a matrix of random samples from the generalized Pareto
distribution wi...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
hygecdf


# name: <cell-element>
# type: sq_string
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# length: 455
 -- hygecdf (X, T, M, N)
     Compute the cumulative distribution function (CDF) at X of the
     hypergeometric distribution with parameters T, M, and N.

     This is the probability of obtaining not more than X marked items
     when randomly drawing a sample of size N without replacement from a
     population of total size T containing M marked items.

     The parameters T, M, and N must be positive integers with M and N
     not greater than T.


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Compute the cumulative distribution function (CDF) at X of the
hypergeometric...



# name: <cell-element>
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# elements: 1
# length: 7
hygeinv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 464
 -- hygeinv (X, T, M, N)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the hypergeometric distribution with parameters T, M,
     and N.

     This is the probability of obtaining X marked items when randomly
     drawing a sample of size N without replacement from a population of
     total size T containing M marked items.

     The parameters T, M, and N must be positive integers with M and N
     not greater than T.


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For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
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# elements: 1
# length: 7
hygepdf


# name: <cell-element>
# type: sq_string
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# length: 1028
 -- PDF = hygepdf (X, T, M, N)
 -- PDF = hygepdf (..., "vectorexpand")
     Compute the probability density function (PDF) at X of the
     hypergeometric distribution with parameters T, M, and N.

     This is the probability of obtaining X marked items when randomly
     drawing a sample of size N without replacement from a population of
     total size T containing M marked items.

     The parameters T, M, and N must be positive integers with M and N
     not greater than T.  They and X may be scalars or arrays, but all
     non-scalars must be the same size.

     The output PDF will be the same size as the input array.

     If the optional parameter 'vectorexpand' is provided, X may be an
     array with size different from parameters T, M, and N (which must
     still be of a common size or scalar).  Each element of X will be
     evaluated against each set of parameters T, M, and N in columnwise
     order.  The output PDF will be an array of size 'R x S', where 'R =
     numel (T)', and 'S = numel (X)'.


# name: <cell-element>
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# elements: 1
# length: 80
Compute the probability density function (PDF) at X of the
hypergeometric dis...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
hygernd


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 -- hygernd (T, M, N)
 -- hygernd (T, M, N, R)
 -- hygernd (T, M, N, R, C, ...)
 -- hygernd (T, M, N, [SZ])
     Return a matrix of random samples from the hypergeometric
     distribution with parameters T, M, and N.

     The parameters T, M, and N must be positive integers with M and N
     not greater than T.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of T, M, and N.


# name: <cell-element>
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Return a matrix of random samples from the hypergeometric distribution
with p...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
iwishpdf


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# length: 668
 -- Function File: Y = iwishpdf (W, TAU, DF, LOG_Y=false)
     Compute the probability density function of the inverse Wishart
     distribution.

     Inputs: A P x P matrix W where to find the PDF and the P x P
     positive definite scale matrix TAU and scalar degrees of freedom
     parameter DF characterizing the inverse Wishart distribution.  (For
     the density to be finite, need DF > (P - 1).)  If the flag LOG_Y is
     set, return the log probability density - this helps avoid
     underflow when the numerical value of the density is very small.

     Output: Y is the probability density of Wishart(SIGMA, DF) at W.

     See also: iwishrnd, wishpdf.


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Compute the probability density function of the inverse Wishart
distribution.



# name: <cell-element>
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# length: 8
iwishrnd


# name: <cell-element>
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# length: 1042
 -- Function File: [W[, DI]] = iwishrnd (PSI, DF[, DI][, N=1])
     Return a random matrix sampled from the inverse Wishart
     distribution with given parameters.

     Inputs: the P x P positive definite matrix TAU and scalar degrees
     of freedom parameter DF (and optionally the transposed Cholesky
     factor DI of SIGMA = 'inv(Tau)').

     DF can be non-integer as long as DF > D

     Output: a random P x P matrix W from the inverse Wishart(TAU, DF)
     distribution.  ('inv(W)' is from the Wishart('inv(Tau)', DF)
     distribution.)  If N > 1, then W is P x P x N and holds N such
     random matrices.  (Optionally, the transposed Cholesky factor DI of
     SIGMA is also returned.)

     Averaged across many samples, the mean of W should approach TAU /
     (DF - P - 1).

     Reference: Yu-Cheng Ku and Peter Bloomfield (2010), Generating
     Random Wishart Matrices with Fractional Degrees of Freedom in OX,
     http://www.gwu.edu/~forcpgm/YuChengKu-030510final-WishartYu-ChengKu.pdf

     See also: wishrnd, iwishpdf.


# name: <cell-element>
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Return a random matrix sampled from the inverse Wishart distribution
with giv...



# name: <cell-element>
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# elements: 1
# length: 6
jsucdf


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# length: 260
 -- Function File: jsucdf (X, ALPHA1, ALPHA2)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Johnson SU distribution with shape parameters
     ALPHA1 and ALPHA2.

     Default values are ALPHA1 = 1, ALPHA2 = 1.


# name: <cell-element>
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For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
jsupdf


# name: <cell-element>
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# length: 256
 -- Function File: jsupdf (X, ALPHA1, ALPHA2)
     For each element of X, compute the probability density function
     (PDF) at X of the Johnson SU distribution with shape parameters
     ALPHA1 and ALPHA2.

     Default values are ALPHA1 = 1, ALPHA2 = 1.


# name: <cell-element>
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# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
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# length: 11
laplace_cdf


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 -- laplace_cdf (X)
 -- laplace_pdf (X, MU, BETA)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Laplace distribution with a location parameter MU
     and a scale parameter (i.e.  "diversity") BETA.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
laplace_inv


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# length: 132
 -- laplace_inv (X)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the Laplace distribution.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
laplace_pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 244
 -- laplace_pdf (X)
 -- laplace_pdf (X, MU, BETA)
     For each element of X, compute the probability density function
     (PDF) at X of the Laplace distribution with a location parameter MU
     and a scale parameter (i.e.  "diversity") BETA.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
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# elements: 1
# length: 11
laplace_rnd


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# length: 509
 -- laplace_rnd (R)
 -- laplace_rnd (R, C, ...)
 -- laplace_rnd ([SZ])
     Return a matrix of random samples from the Laplace distribution.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.


# name: <cell-element>
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# length: 64
Return a matrix of random samples from the Laplace distribution.



# name: <cell-element>
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# length: 12
logistic_cdf


# name: <cell-element>
# type: sq_string
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# length: 215
 -- logistic_cdf (X)
 -- logistic_cdf (X, MU, SCALE)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the logistic distribution with mean MU and scale
     parameter SCALE.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
logistic_inv


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# length: 210
 -- logistic_inv (X)
 -- logistic_pdf (X, MU, SCALE)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the logistic distribution with mean MU and scale
     parameter SCALE.


# name: <cell-element>
# type: sq_string
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# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
logistic_pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 175
 -- logistic_pdf (X)
 -- logistic_pdf (X, MU, SCALE)
     For each element of X, compute the PDF at X of the logistic
     distribution with mean MU and scale parameter SCALE.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the PDF at X of the logistic distribution
with...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
logistic_rnd


# name: <cell-element>
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# length: 513
 -- logistic_rnd (R)
 -- logistic_rnd (R, C, ...)
 -- logistic_rnd ([SZ])
     Return a matrix of random samples from the logistic distribution.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.


# name: <cell-element>
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Return a matrix of random samples from the logistic distribution.



# name: <cell-element>
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# length: 7
logncdf


# name: <cell-element>
# type: sq_string
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# length: 380
 -- logncdf (X)
 -- logncdf (X, MU, SIGMA)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the lognormal distribution with parameters MU and
     SIGMA.

     If a random variable follows this distribution, its logarithm is
     normally distributed with mean MU and standard deviation SIGMA.

     Default values are MU = 0, SIGMA = 1.


# name: <cell-element>
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# elements: 1
# length: 80
For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
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# elements: 1
# length: 7
logninv


# name: <cell-element>
# type: sq_string
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 -- logninv (X)
 -- logninv (X, MU, SIGMA)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the lognormal distribution with parameters MU and
     SIGMA.

     If a random variable follows this distribution, its logarithm is
     normally distributed with mean MU and standard deviation SIGMA.

     Default values are MU = 0, SIGMA = 1.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
lognpdf


# name: <cell-element>
# type: sq_string
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 -- lognpdf (X)
 -- lognpdf (X, MU, SIGMA)
     For each element of X, compute the probability density function
     (PDF) at X of the lognormal distribution with parameters MU and
     SIGMA.

     If a random variable follows this distribution, its logarithm is
     normally distributed with mean MU and standard deviation SIGMA.

     Default values are MU = 0, SIGMA = 1.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
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# elements: 1
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lognrnd


# name: <cell-element>
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 -- lognrnd (MU, SIGMA)
 -- lognrnd (MU, SIGMA, R)
 -- lognrnd (MU, SIGMA, R, C, ...)
 -- lognrnd (MU, SIGMA, [SZ])
     Return a matrix of random samples from the lognormal distribution
     with parameters MU and SIGMA.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of MU and SIGMA.


# name: <cell-element>
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# length: 80
Return a matrix of random samples from the lognormal distribution with
parame...



# name: <cell-element>
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# elements: 1
# length: 5
mnpdf


# name: <cell-element>
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 -- Function File: Y = mnpdf (X, P)
     Compute the probability density function of the multinomial
     distribution.

     Arguments
     ---------

        * X is vector with a single sample of a multinomial distribution
          with parameter P or a matrix of random samples from
          multinomial distributions.  In the latter case, each row of X
          is a sample from a multinomial distribution with the
          corresponding row of P being its parameter.

        * P is a vector with the probabilities of the categories or a
          matrix with each row containing the probabilities of a
          multinomial sample.

     Return values
     -------------

        * Y is a vector of probabilites of the random samples X from the
          multinomial distribution with corresponding parameter P.  The
          parameter N of the multinomial distribution is the sum of the
          elements of each row of X.  The length of Y is the number of
          columns of X.  If a row of P does not sum to '1', then the
          corresponding element of Y will be 'NaN'.

     Examples
     --------

          x = [1, 4, 2];
          p = [0.2, 0.5, 0.3];
          y = mnpdf (x, p);

          x = [1, 4, 2; 1, 0, 9];
          p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8];
          y = mnpdf (x, p);

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  'Computational
          Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Merran Evans, Nicholas Hastings and Brian Peacock.
          'Statistical Distributions'.  pages 134-136, Wiley, New York,
          third edition, 2000.


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Compute the probability density function of the multinomial
distribution.



# name: <cell-element>
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# length: 5
mnrnd


# name: <cell-element>
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 -- Function File: X = mnrnd (N, P)
 -- Function File: X = mnrnd (N, P, S)
     Generate random samples from the multinomial distribution.

     Arguments
     ---------

        * N is the first parameter of the multinomial distribution.  N
          can be scalar or a vector containing the number of trials of
          each multinomial sample.  The elements of N must be
          non-negative integers.

        * P is the second parameter of the multinomial distribution.  P
          can be a vector with the probabilities of the categories or a
          matrix with each row containing the probabilities of a
          multinomial sample.  If P has more than one row and N is
          non-scalar, then the number of rows of P must match the number
          of elements of N.

        * S is the number of multinomial samples to be generated.  S
          must be a non-negative integer.  If S is specified, then N
          must be scalar and P must be a vector.

     Return values
     -------------

        * X is a matrix of random samples from the multinomial
          distribution with corresponding parameters N and P.  Each row
          corresponds to one multinomial sample.  The number of columns,
          therefore, corresponds to the number of columns of P.  If S is
          not specified, then the number of rows of X is the maximum of
          the number of elements of N and the number of rows of P.  If a
          row of P does not sum to '1', then the corresponding row of X
          will contain only 'NaN' values.

     Examples
     --------

          n = 10;
          p = [0.2, 0.5, 0.3];
          x = mnrnd (n, p);

          n = 10 * ones (3, 1);
          p = [0.2, 0.5, 0.3];
          x = mnrnd (n, p);

          n = (1:2)';
          p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8];
          x = mnrnd (n, p);

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  'Computational
          Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Merran Evans, Nicholas Hastings and Brian Peacock.
          'Statistical Distributions'.  pages 134-136, Wiley, New York,
          third edition, 2000.


# name: <cell-element>
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Generate random samples from the multinomial distribution.



# name: <cell-element>
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mvncdf


# name: <cell-element>
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 -- Function File: Y = mvncdf (X)
 -- Function File: Y = mvncdf (X, MU, SIGMA)
 -- Function File: Y = mvncdf (X_LO, X_UP, MU, SIGMA)
 -- Function File: Y = mvncdf (..., OPTIONS)
 -- Function File: [Y, ERR] = mvncdf (...)

     Multivariate normal cumulative distribution function.

     'Y = mvncdf (X)' returns cumulative probability of the multivariate
     normal distribution evaluated at each row of X with zero mean and
     an identity covariance matrix.  The row of matrix X correspond to
     observations and its columns to variables.  The return argument Y
     is a column vector with the same number of rows as in X.

     'Y = mvncdf (X, MU, SIGMA)' returns cumulative probability of the
     multivariate normal distribution evaluated at each row of X with
     mean MU and a covariance matrix SIGMA.  MU can be either a scalar
     (the same of every variable) or a row vector with the same number
     of elements as the number of variables in X.  SIGMA covariance
     matrix may be specified a row vector if it only contains variances
     along its diagonal and zero covariances of the diagonal.  In such a
     case, the diagonal vector SIGMA must have the same number of
     elements as the number of variables (columns) in X.  If you only
     want to specify sigma, you can pass an empty matrix for MU.

     The multivariate normal cumulative probability at X is defined as
     the probability that a random vector V, distributed as multivariate
     normal, will fall within the semi-infinite rectangle with upper
     limits defined by X.
        * Pr{V(1)<=X(1), V(2)<=X(2), ...  V(D)<=X(D)}.

     'Y = mvncdf (X_LO, X_HI, MU, SIGMA)' returns the multivariate
     normal cumulative probability evaluated over the rectangle
     (hyper-rectangle for multivariate data in X) with lower and upper
     limits defined by X_LO and X_HI respectively.

     '[Y, ERR] = mvncdf (...)' also returns an error estimate ERR in Y.

     'Y = mvncdf (..., OPTIONS)' specifies the structure, which controls
     specific parameters for the numerical integration for numltivariate
     cases.  The required fieds are:

     "TolFun"       -- Maximum absolute error tolerance.  Default is 1e-8
                    for D == 1 | 3, 1e-4 for D > 4.  Note that for bivariate
                    normal cdf, the Octave implementation has a presicion of
                    more than 1e-10.
     "MaxFunEvals"  -- Maximum number of integrand evaluations.  Default is
                    1e7 for D > 4.
     "Display"      -- Display options.  Choices are "off" (default),
                    "iter", which shows the probability and estimated error
                    at each repetition, and "final", which shows the final
                    probability and related error after the integrand has
                    converged successfully.


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Multivariate normal cumulative distribution function.



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mvnpdf


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 -- statistics: Y = mvnpdf (X, MU, SIGMA)

     Multivariate normal probability density function (pdf).

     'Y = mvnpdf (X)' returns the probability density of the
     multivariate normal distribution with zero mean and identity
     covariance matrix, evaluated at each row of X.  Rows of the N-by-D
     matrix X correspond to observations orpoints, and columns
     correspond to variables or coordinates.  Y is an N-by-1 vector.

     'Y = mvnpdf (X, MU)' returns the density of the multivariate normal
     distribution with mean MU and identity covariance matrix, evaluated
     at each row of X.  MU is a 1-by-D vector, or an N-by-D matrix, in
     which case the density is evaluated for each row of X with the
     corresponding row of MU.  MU can also be a scalar value, which
     MVNPDF replicates to match the size of X.

     'Y = mvnpdf (X, MU, SIGMA)' returns the density of the multivariate
     normal distribution with mean MU and covariance SIGMA, evaluated at
     each row of X.  SIGMA is a D-by-D matrix, or an D-by-D-by-N array,
     in which case the density is evaluated for each row of X with the
     corresponding page of SIGMA, i.e., 'mcvpdf' computes Y(I) using
     X(I,:) and SIGMA(:,:,I).  If the covariance matrix is diagonal,
     containing variances along the diagonal and zero covariances off
     the diagonal, SIGMA may also be specified as a 1-by-D matrix or a
     1-by-D-by-N array, containing just the diagonal.  Pass in the empty
     matrix for MU to use its default value when you want to only
     specify SIGMA.

     If X is a 1-by-D vector, 'mcvpdf' replicates it to match the
     leading dimension of MU or the trailing dimension of SIGMA.

     See also: mvncdf, mvnrnd, normpdf, pdf.


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Multivariate normal probability density function (pdf).



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mvnrnd


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 -- statistics: R = mvnrnd (MU, SIGMA)
 -- statistics: R = mvnrnd (MU, SIGMA, N)
 -- statistics: R = mvnrnd (MU, SIGMA, N, T)
 -- statistics: [R, T] = mvnrnd (...)

     Random vectors from the multivariate normal distribution.

     'R = mvnrnd (MU, SIGMA)' returns an N-by-D matrix R of random
     vectors chosen from the multivariate normal distribution with mean
     vector MU and covariance matrix SIGMA.  MU is an N-by-D matrix, and
     'mvnrnd' generates each N of R using the corresponding N of MU.
     SIGMA is a D-by-D symmetric positive semi-definite matrix, or a
     D-by-D-by-N array.  If SIGMA is an array, 'mvnrnd' generates each N
     of R using the corresponding page of SIGMA, i.e., 'mvnrnd' computes
     R(I,:) using MU(I,:) and SIGMA(:,:,I).  If the covariance matrix is
     diagonal, containing variances along the diagonal and zero
     covariances off the diagonal, SIGMA may also be specified as a
     1-by-D matrix or a 1-by-D-by-N array, containing just the diagonal.
     If MU is a 1-by-D vector, 'mvnrnd' replicates it to match the
     trailing dimension of SIGMA.

     'R = mvnrnd (MU, SIGMA, N)' returns a N-by-D matrix R of random
     vectors chosen from the multivariate normal distribution with
     1-by-D mean vector MU, and D-by-D covariance matrix SIGMA.

     'R = mvnrnd (MU, SIGMA, N, T)' supplies the Cholesky factor T of
     SIGMA, so that SIGMA(:,:,J) == T(:,:,J)'*T(:,:,J) if SIGMA is a 3D
     array or SIGMA == T'*T if SIGMA is a matrix.  No error checking is
     done on T.

     '[R, T] = mvnrnd (...)' returns the Cholesky factor T, so it can be
     re-used to make later calls more efficient, although there are
     greater efficiency gains when SIGMA can be specified as a diagonal
     instead.

     See also: mvncdf, mvnpdf, normrnd, random.


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Random vectors from the multivariate normal distribution.



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mvtcdf


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 -- Function File: P = mvtcdf (X, SIGMA, NU)
 -- Function File: mvtcdf (A, X, SIGMA, NU)
 -- Function File: [P, ERR] = mvtcdf (...)
     Compute the cumulative distribution function of the multivariate
     Student's t distribution.

     Arguments
     ---------

        * X is the upper limit for integration where each row
          corresponds to an observation.

        * SIGMA is the correlation matrix.

        * NU is the degrees of freedom.

        * A is the lower limit for integration where each row
          corresponds to an observation.  A must have the same size as
          X.

     Return values
     -------------

        * P is the cumulative distribution at each row of X and A.

        * ERR is the estimated error.

     Examples
     --------

          x = [1 2];
          sigma = [1.0 0.5; 0.5 1.0];
          nu = 4;
          p = mvtcdf (x, sigma, nu)

          a = [-inf 0];
          p = mvtcdf (a, x, sigma, nu)

     References
     ----------

       1. Alan Genz and Frank Bretz.  Numerical Computation of
          Multivariate t-Probabilities with Application to Power
          Calculation of Multiple Constrasts.  'Journal of Statistical
          Computation and Simulation', 63, pages 361-378, 1999.


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Compute the cumulative distribution function of the multivariate
Student's t ...



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mvtcdfqmc


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 -- Function File: P = mvtcdfqmc (A, B, RHO, DF)
 -- Function File: P = mvtcdfqmc (..., TOLFUN)
 -- Function File: P = mvtcdfqmc (..., TOLFUN, MAXFUNEVALS)
 -- Function File: P = mvtcdfqmc (..., TOLFUN, MAXFUNEVALS, DISPLAY)
 -- Function File: [P, ERR] = mvncdf (...)
 -- Function File: [P, ERR, FUNEVALS] = mvncdf (...)

     Quasi-Monte-Carlo computation of the multivariate Student's t cdf.

     The QMC multivariate Student's t distribution is evaluated between
     the lower limit A and upper limit B of the hyper-rectangle with a
     correlation matrix RHO and degrees of freedom DF.

     "TolFun"       -- Maximum absolute error tolerance.  Default is 1e-4.
     "MaxFunEvals"  -- Maximum number of integrand evaluations.  Default is
                    1e7 for D > 4.
     "Display"      -- Display options.  Choices are "off" (default),
                    "iter", which shows the probability and estimated error
                    at each repetition, and "final", which shows the final
                    probability and related error after the integrand has
                    converged successfully.

     '[P, ERR, FUNEVALS] = mvncdf (...)' returns the estimated
     probability, P, an estimate of the error, ERR, and the number of
     iterations until a successful convergence is met, unless the value
     in MAXFUNEVALS was reached.


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Quasi-Monte-Carlo computation of the multivariate Student's t cdf.



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mvtpdf


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 -- Function File: P = mvtpdf (X, SIGMA, NU)
     Compute the probability density function of the multivariate
     Student's t distribution.

     Arguments
     ---------

        * X are the points at which to find the probability, where each
          row corresponds to an observation.  (N by D matrix)

        * SIGMA is the scale matrix.  (D by D symmetric positive
          definite matrix)

        * NU is the degrees of freedom.  (scalar or N vector)

     The distribution is assumed to be centered (zero mean).

     Return values
     -------------

        * P is the probability density for each row of X.  (N by 1
          vector)

     Examples
     --------

          x = [1 2];
          sigma = [1.0 0.5; 0.5 1.0];
          nu = 4;
          p = mvtpdf (x, sigma, nu)

     References
     ----------

       1. Michael Roth, On the Multivariate t Distribution, Technical
          report from Automatic Control at Linkoepings universitet,
          <http://users.isy.liu.se/en/rt/roth/student.pdf>


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Compute the probability density function of the multivariate Student's t
dist...



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mvtrnd


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 -- Function File: X = mvtrnd (SIGMA, NU)
 -- Function File: X = mvtrnd (SIGMA, NU, N)
     Generate random samples from the multivariate t-distribution.

     Arguments
     ---------

        * SIGMA is the matrix of correlation coefficients.  If there are
          any non-unit diagonal elements then SIGMA will be normalized,
          so that the resulting covariance of the obtained samples X
          follows: 'cov (x) = nu/(nu-2) * sigma ./ (sqrt (diag (sigma) *
          diag (sigma)))'.  In order to obtain samples distributed
          according to a standard multivariate t-distribution, SIGMA
          must be equal to the identity matrix.  To generate
          multivariate t-distribution samples X with arbitrary
          covariance matrix SIGMA, the following scaling might be used:
          'x = mvtrnd (sigma, nu, n) * diag (sqrt (diag (sigma)))'.

        * NU is the degrees of freedom for the multivariate
          t-distribution.  NU must be a vector with the same number of
          elements as samples to be generated or be scalar.

        * N is the number of rows of the matrix to be generated.  N must
          be a non-negative integer and corresponds to the number of
          samples to be generated.

     Return values
     -------------

        * X is a matrix of random samples from the multivariate
          t-distribution with N row samples.

     Examples
     --------

          sigma = [1, 0.5; 0.5, 1];
          nu = 3;
          n = 10;
          x = mvtrnd (sigma, nu, n);

          sigma = [1, 0.5; 0.5, 1];
          nu = [2; 3];
          n = 2;
          x = mvtrnd (sigma, nu, 2);

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  'Computational
          Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Samuel Kotz and Saralees Nadarajah.  'Multivariate t
          Distributions and Their Applications'.  Cambridge University
          Press, Cambridge, 2004.


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Generate random samples from the multivariate t-distribution.



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nakacdf


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 -- nakacdf (X, M, W)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Nakagami distribution with shape parameter M and
     scale parameter W.


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For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
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# length: 7
nakainv


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 -- nakainv (X, M, W)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the Nakagami distribution with shape parameter M and
     scale parameter W.


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For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
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# length: 7
nakapdf


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 -- nakapdf (X, M, W)
     For each element of X, compute the probability density function
     (PDF) at X of the Nakagami distribution with shape parameter M and
     scale parameter W.


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For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
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nakarnd


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 -- nakarnd (M, W)
 -- nakarnd (M, W, R)
 -- nakarnd (M, W, R, C, ...)
 -- nakarnd (M, W, [SZ])
     Return a matrix of random samples from the Nakagami distribution
     with shape parameter M and scale W.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of M and W.


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Return a matrix of random samples from the Nakagami distribution with
shape p...



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# elements: 1
# length: 7
nbincdf


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 -- nbincdf (X, N, P)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the negative binomial distribution with parameters N
     and P.

     When N is integer this is the Pascal distribution.  When N is
     extended to real numbers this is the Polya distribution.

     The number of failures in a Bernoulli experiment with success
     probability P before the N-th success follows this distribution.


# name: <cell-element>
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For each element of X, compute the cumulative distribution function
(CDF) at ...



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nbininv


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 -- nbininv (X, N, P)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the negative binomial distribution with parameters N
     and P.

     When N is integer this is the Pascal distribution.  When N is
     extended to real numbers this is the Polya distribution.

     The number of failures in a Bernoulli experiment with success
     probability P before the N-th success follows this distribution.


# name: <cell-element>
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For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
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# elements: 1
# length: 7
nbinpdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 442
 -- nbinpdf (X, N, P)
     For each element of X, compute the probability density function
     (PDF) at X of the negative binomial distribution with parameters N
     and P.

     When N is integer this is the Pascal distribution.  When N is
     extended to real numbers this is the Polya distribution.

     The number of failures in a Bernoulli experiment with success
     probability P before the N-th success follows this distribution.


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# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



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nbinrnd


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 -- nbinrnd (N, P)
 -- nbinrnd (N, P, R)
 -- nbinrnd (N, P, R, C, ...)
 -- nbinrnd (N, P, [SZ])
     Return a matrix of random samples from the negative binomial
     distribution with parameters N and P.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of N and P.


# name: <cell-element>
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Return a matrix of random samples from the negative binomial
distribution wit...



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ncfcdf


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 -- Function File: P = ncfcdf (X, DF1, DF2, DELTA)
 -- Function File: P = ncfcdf (X, DF1, DF2, DELTA, UFLAG)

     Noncentral F cumulative distribution function (cdf).

     'P = ncfcdf (X, DF1, DF2, DELTA)' returns the noncentral F cdf with
     DF degrees of freedom and noncentrality parameter DELTA at the
     values of X.

     The size of P is the common size of the input arguments.  Scalar
     input arguments X, DF1, DF2, DELTA are regarded as constant
     matrices of the same size as the other inputs.

     'P = ncfcdf (X, DF1, DF2, DELTA, "upper"' returns the upper tail
     probability of the noncentral T distribution with DF1 and DF2
     degrees of freedom and noncentrality parameter DELTA at the values
     in X.

     See also: ncfinv, ncfpdf, ncfrnd, ncfstat.


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Noncentral F cumulative distribution function (cdf).



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ncfinv


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 -- Function File: X = ncfinv (P, DF1, DF2, DELTA)

     Inverse of the non-central F cumulative distribution function
     (cdf).

     'X = ncfinv (P, DF1, DF2, DELTA)' the inverse of the noncentral F
     distribution with DF1 numerator degrees of freedom, DF2 denumerator
     degrees of freedom, and noncentrality parameter DELTA, at the
     probabilities of P.

     The size of X is the common size of DF and DELTA.  A scalar input
     functions as a constant matrix of the same size as the other
     inputs.

     'ncfinv' uses Newton's method to converge to the solution.

     See also: ncfcdf, ncfpdf, ncfrnd, ncfstat.


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Inverse of the non-central F cumulative distribution function (cdf).



# name: <cell-element>
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# length: 6
ncfpdf


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 -- Function File: Y = ncfpdf (X, DF1, DF2, DELTA)

     Noncentral F probability density function (pdf).

     'Y = ncfpdf (X, DF1, DF2, DELTA)' returns the noncentral F
     distribution with DF1 and DF2 numerator and denumerator degrees of
     freedom, respectively, and noncentrality parameter DELTA, at the
     values of X.

     The size of Y is the common size of DF and DELTA.  A scalar input
     functions as a constant matrix of the same size as the K_all
     inputs.

     See also: ncfcdf, ncfinv, ncfrnd, ncfstat.


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Noncentral F probability density function (pdf).



# name: <cell-element>
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ncfrnd


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 -- Function File: R = ncfrnd (DF1, DF2, DELTA)
 -- Function File: R = ncfrnd (DF1, DF2, DELTA, M, N, ...)
 -- Function File: R = ncfrnd (DF1, DF2, DELTA, [M, N, ...])

     Random arrays from the noncentral F distribution.

     'X = ncfrnd (P, DF1, DF2, DELTA)' returns an array of random
     numbers chosen from the noncentral F distribution with parameters
     DF1, DF2, DELTA).  The size of R is the common size of DF1, DF2,
     and DELTA.  A scalar input functions as a constant matrix of the
     same size as the other input.

     'R = ncfrnd (DF1, DF2, DELTA, M, N, ...)' or 'R = ncfrnd (DF1, DF2,
     DELTA, [M, N, ...])' returns an M-by-N-by-...  array.

     'ncfrnd' generates values using the definition of a noncentral F
     random variable, as the ratio of a noncentral chi-square and a
     (central) chi-square.

     See also: ncfcdf, ncfinv, ncfpdf, ncfstat.


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Random arrays from the noncentral F distribution.



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nctcdf


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 -- Function File: P = nctcdf (X, DF, DELTA)
 -- Function File: P = nctcdf (X, DF, DELTA, UFLAG)

     Noncentral T cumulative distribution function (cdf).

     'P = nctcdf (X, DF, DELTA)' returns the noncentral T cdf with DF
     degrees of freedom and noncentrality parameter DELTA at the values
     of X.

     The size of P is the common size of the input arguments.  Scalar
     input arguments X, DF, DELTA are regarded as constant matrices of
     the same size as the other inputs.

     'P = nctcdf (X, DF, DELTA, "upper"' returns the upper tail
     probability of the noncentral T distribution with DF degrees of
     freedom and noncentrality parameter DELTA at the values in X.

     See also: nctinv, nctpdf, nctrnd, nctstat.


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Noncentral T cumulative distribution function (cdf).



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nctinv


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 -- Function File: X = ncx2inv (P, DF, DELTA)

     Inverse of the non-central T cumulative distribution function
     (cdf).

     'X = nctinv (P, DF, DELTA)' returns the inverse of the noncentral T
     cdf with DF degrees of freedom and noncentrality parameter DELTA,
     at the probabilities of P.

     The size of X is the common size of DF and DELTA.  A scalar input
     functions as a constant matrix of the same size as the other
     inputs.

     'nctinv' uses Newton's method to converge to the solution.

     See also: nctcdf, nctpdf, nctrnd, nctstat.


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Inverse of the non-central T cumulative distribution function (cdf).



# name: <cell-element>
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nctpdf


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 -- statistics: Y = nctpdf (X, DF, DELTA)

     Noncentral ??  probability density function (pdf).

     'Y = nctpdf (X, DF, DELTA)' returns the noncentral T distribution
     with DF degrees of freedom and noncentrality parameter DELTA, at
     the values of X.

     The size of Y is the common size of DF and DELTA.  A scalar input
     functions as a constant matrix of the same size as the K_all
     inputs.

     See also: nctcdf, nctinv, nctrnd, nctstat, tpdf, pdf.


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Noncentral ??  probability density function (pdf).



# name: <cell-element>
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# length: 6
nctrnd


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 -- Function File: R = nctrnd (DF, DELTA)
 -- Function File: R = nctrnd (DF, DELTA, M, N, ...)
 -- Function File: R = nctrnd (DF, DELTA, [M, N, ...])

     Random arrays from the noncentral T distribution.

     'X = nctrnd (P, DF, DELTA)' returns an array of random numbers
     chosen from the noncentral F distribution with parameters DF1, DF2,
     DELTA).  The size of R is the common size of DF1, DF2, and DELTA.
     A scalar input functions as a constant matrix of the same size as
     the other input.

     'R = nctrnd (DF, DELTA, M, N, ...)' or 'R = nctrnd (DF, DELTA, [M,
     N, ...])' returns an M-by-N-by-...  array.

     'nctrnd' generates values using the definition of a noncentral T
     random variable, as the ratio of a normal with non-zero mean and
     the sqrt of a chi-square.

     See also: nctcdf, nctinv, nctpdf, nctstat.


# name: <cell-element>
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Random arrays from the noncentral T distribution.



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ncx2cdf


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 -- Function File: P = ncx2cdf (X, DF, DELTA)
 -- Function File: P = ncx2cdf (X, DF, DELTA, UFLAG)

     Noncentral Chi-Square cumulative distribution function (cdf).

     'P = ncx2cdf (X, DF, DELTA)' returns the noncentral chi-square cdf
     with DF degrees of freedom and noncentrality parameter DELTA at the
     values of X.

     The size of P is the common size of the input arguments.  Scalar
     input arguments X, DF, DELTA are regarded as constant matrices of
     the same size as the other inputs.

     'P = ncx2cdf (X, DF, DELTA, "upper"' returns the upper tail
     probability of the noncentral chi-square distribution with DF
     degrees of freedom and noncentrality parameter DELTA at the values
     in X.

     See also: ncx2inv, ncx2pdf, ncx2rnd, ncx2stat.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Noncentral Chi-Square cumulative distribution function (cdf).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
ncx2inv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 600
 -- Function File: X = ncx2inv (P, DF, DELTA)

     Inverse of the non-central chi-square cumulative distribution
     function (cdf).

     'X = ncx2inv (P, DF, DELTA)' returns the inverse of the noncentral
     chi-square distribution with DF degrees of freedom and
     noncentrality parameter DELTA, at the probabilities of P.

     The size of X is the common size of DF and DELTA.  A scalar input
     functions as a constant matrix of the same size as the other
     inputs.

     'ncx2inv' uses Newton's method to converge to the solution.

     See also: ncx2cdf, ncx2pdf, ncx2rnd, ncx2stat.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 77
Inverse of the non-central chi-square cumulative distribution function
(cdf).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
ncx2pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 513
 -- Function File: Y = ncx2pdf (X, DF, DELTA)

     Noncentral Chi-Square probability distribution function (pdf).

     'Y = ncx2pdf (X, DF, DELTA)' returns the noncentral chi-square pdf
     with DF degrees of freedom and noncentrality parameter DELTA at the
     values of X.

     The size of Y is the common size of the input arguments.  Scalar
     input arguments X, DF, DELTA are regarded as constant matrices of
     the same size as the other inputs.

     See also: ncx2cdf, ncx2inv, ncx2rnd, ncx2stat.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Noncentral Chi-Square probability distribution function (pdf).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
ncx2rnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 730
 -- Function File: R = ncx2rnd (DF, DELTA)
 -- Function File: R = ncx2rnd (DF, DELTA, M, N, ...)
 -- Function File: R = ncx2rnd (DF, DELTA, [M, N, ...])

     Random arrays from the non-central chi-square distribution.

     'R = ncx2rnd (DF, DELTA)' returns an array of random numbers chosen
     from the non-central chi-square distribution with DF degrees of
     freedom and noncentrality parameter DELTA.  The size of R is the
     common size of DF and DELTA.  A scalar input functions as a
     constant matrix of the same size as the other input.

     'R = ncx2rnd (DF, DELTA, M, N, ...)' or 'R = ncx2rnd (DF, DELTA,
     [M, N, ...])' returns an M-by-N-by-...  array.

     See also: ncx2cdf, ncx2inv, ncx2pdf, ncx2stat.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 59
Random arrays from the non-central chi-square distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
normcdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1588
 -- Function File: P = normcdf (X)
 -- Function File: P = normcdf (X, MU)
 -- Function File: P = normcdf (X, MU, SIGMA)
 -- Function File: P = normcdf (..., "upper")
 -- Function File: [P, PLO, PUP] = normcdf (X, MU, SIGMA, PCOV)
 -- Function File: [P, PLO, PUP] = normcdf (X, MU, SIGMA, PCOV, ALPHA)
 -- Function File: [P, PLO, PUP] = normcdf (..., "upper")

     Normal cumulative distribution function (cdf).

     For each element of X, compute the cumulative distribution function
     (CDF) at X of the normal distribution with mean MU and standard
     deviation SIGMA.  The size of P is the common size of X, MU and
     SIGMA.  A scalar input functions as a constant matrix of the same
     size as the other inputs.

     Default values are MU = 0, SIGMA = 1.

     When called with three output arguments, '[P, PLO, PUP]' it
     computes the confidence bounds for P when the input parameters MU
     and SIGMA are estimates.  In such case, PCOV, a 2-by-2 matrix
     containing the covariance matrix of the estimated parameters, is
     necessary.  Optionally, ALPHA has a default value of 0.05, and
     specifies 100 * (1 - ALPHA)% confidence bounds.  PLO and PUP are
     arrays of the same size as P containing the lower and upper
     confidence bounds.

     '[...] = normcdf (..., "upper")' computes the upper tail
     probability of the normal distribution.  This can be used to
     compute a right-tailed p-value.  To compute a two-tailed p-value,
     use '2 * normcdf (-abs (X), MU, SIGMA)'.

     See also: norminv, normpdf, normrnd, normfit, normlike, normstat.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Normal cumulative distribution function (cdf).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
norminv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 245
 -- norminv (X)
 -- norminv (X, MU, SIGMA)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the normal distribution with mean MU and standard
     deviation SIGMA.

     Default values are MU = 0, SIGMA = 1.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
normpdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 246
 -- normpdf (X)
 -- normpdf (X, MU, SIGMA)
     For each element of X, compute the probability density function
     (PDF) at X of the normal distribution with mean MU and standard
     deviation SIGMA.

     Default values are MU = 0, SIGMA = 1.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
normrnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 712
 -- normrnd (MU, SIGMA)
 -- normrnd (MU, SIGMA, R)
 -- normrnd (MU, SIGMA, R, C, ...)
 -- normrnd (MU, SIGMA, [SZ])
     Return a matrix of random samples from the normal distribution with
     parameters mean MU and standard deviation SIGMA.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of MU and SIGMA.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return a matrix of random samples from the normal distribution with
parameter...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
poisscdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 164
 -- poisscdf (X, LAMBDA)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the Poisson distribution with parameter LAMBDA.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
poissinv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 159
 -- poissinv (X, LAMBDA)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the Poisson distribution with parameter LAMBDA.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
poisspdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 160
 -- poisspdf (X, LAMBDA)
     For each element of X, compute the probability density function
     (PDF) at X of the Poisson distribution with parameter LAMBDA.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
poissrnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 661
 -- poissrnd (LAMBDA)
 -- poissrnd (LAMBDA, R)
 -- poissrnd (LAMBDA, R, C, ...)
 -- poissrnd (LAMBDA, [SZ])
     Return a matrix of random samples from the Poisson distribution
     with parameter LAMBDA.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the size
     of LAMBDA.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return a matrix of random samples from the Poisson distribution with
paramete...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
raylcdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1119
 -- Function File: P = raylcdf (X, SIGMA)
     Compute the cumulative distribution function of the Rayleigh
     distribution.

     Arguments
     ---------

        * X is the support.  The elements of X must be non-negative.

        * SIGMA is the parameter of the Rayleigh distribution.  The
          elements of SIGMA must be positive.
     X and SIGMA must be of common size or one of them must be scalar.

     Return values
     -------------

        * P is the cumulative distribution of the Rayleigh distribution
          at each element of X and corresponding parameter SIGMA.

     Examples
     --------

          x = 0:0.5:2.5;
          sigma = 1:6;
          p = raylcdf (x, sigma)

          p = raylcdf (x, 0.5)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  'Computational
          Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  'Probability, Random Variables, and
          Stochastic Processes'.  pages 104 and 148, McGraw-Hill, New
          York, second edition, 1984.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 74
Compute the cumulative distribution function of the Rayleigh
distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
raylinv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1177
 -- Function File: X = raylinv (P, SIGMA)
     Compute the quantile of the Rayleigh distribution.  The quantile is
     the inverse of the cumulative distribution function.

     Arguments
     ---------

        * P is the cumulative distribution.  The elements of P must be
          probabilities.

        * SIGMA is the parameter of the Rayleigh distribution.  The
          elements of SIGMA must be positive.
     P and SIGMA must be of common size or one of them must be scalar.

     Return values
     -------------

        * X is the quantile of the Rayleigh distribution at each element
          of P and corresponding parameter SIGMA.

     Examples
     --------

          p = 0:0.1:0.5;
          sigma = 1:6;
          x = raylinv (p, sigma)

          x = raylinv (p, 0.5)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  'Computational
          Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  'Probability, Random Variables, and
          Stochastic Processes'.  pages 104 and 148, McGraw-Hill, New
          York, second edition, 1984.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
Compute the quantile of the Rayleigh distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
raylpdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1111
 -- Function File: Y = raylpdf (X, SIGMA)
     Compute the probability density function of the Rayleigh
     distribution.

     Arguments
     ---------

        * X is the support.  The elements of X must be non-negative.

        * SIGMA is the parameter of the Rayleigh distribution.  The
          elements of SIGMA must be positive.
     X and SIGMA must be of common size or one of them must be scalar.

     Return values
     -------------

        * Y is the probability density of the Rayleigh distribution at
          each element of X and corresponding parameter SIGMA.

     Examples
     --------

          x = 0:0.5:2.5;
          sigma = 1:6;
          y = raylpdf (x, sigma)

          y = raylpdf (x, 0.5)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  'Computational
          Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  'Probability, Random Variables, and
          Stochastic Processes'.  pages 104 and 148, McGraw-Hill, New
          York, second edition, 1984.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 70
Compute the probability density function of the Rayleigh distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
raylrnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1525
 -- Function File: X = raylrnd (SIGMA)
 -- Function File: X = raylrnd (SIGMA, SZ)
 -- Function File: X = raylrnd (SIGMA, R, C)
     Generate a matrix of random samples from the Rayleigh distribution.

     Arguments
     ---------

        * SIGMA is the parameter of the Rayleigh distribution.  The
          elements of SIGMA must be positive.

        * SZ is the size of the matrix to be generated.  SZ must be a
          vector of non-negative integers.

        * R is the number of rows of the matrix to be generated.  R must
          be a non-negative integer.

        * C is the number of columns of the matrix to be generated.  C
          must be a non-negative integer.

     Return values
     -------------

        * X is a matrix of random samples from the Rayleigh distribution
          with corresponding parameter SIGMA.  If neither SZ nor R and C
          are specified, then X is of the same size as SIGMA.

     Examples
     --------

          sigma = 1:6;
          x = raylrnd (sigma)

          sz = [2, 3];
          x = raylrnd (0.5, sz)

          r = 2;
          c = 3;
          x = raylrnd (0.5, r, c)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  'Computational
          Statistics Handbook with MATLAB'. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  'Probability, Random Variables, and
          Stochastic Processes'.  pages 104 and 148, McGraw-Hill, New
          York, second edition, 1984.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
Generate a matrix of random samples from the Rayleigh distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
stdnormal_cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 187
 -- stdnormal_cdf (X)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the standard normal distribution (mean = 0, standard
     deviation = 1).


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
stdnormal_inv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 182
 -- stdnormal_inv (X)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the standard normal distribution (mean = 0, standard
     deviation = 1).


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
stdnormal_pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 183
 -- stdnormal_pdf (X)
     For each element of X, compute the probability density function
     (PDF) at X of the standard normal distribution (mean = 0, standard
     deviation = 1).


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
stdnormal_rnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 563
 -- stdnormal_rnd (R)
 -- stdnormal_rnd (R, C, ...)
 -- stdnormal_rnd ([SZ])
     Return a matrix of random samples from the standard normal
     distribution (mean = 0, standard deviation = 1).

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return a matrix of random samples from the standard normal distribution
(mean...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
tcdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 635
 -- Function File: P = tcdf (X, DF)
 -- Function File: P = tcdf (X, DF, "upper")

     Student's T cumulative distribution function (cdf).

     For each element of X, compute the cumulative distribution function
     (CDF) at X of the t (Student) distribution with DF degrees of
     freedom.

     The size of P is the common size of X and DF.  A scalar input
     functions as a constant matrix of the same size as the other input.

     'P = tcdf (X, DF, "upper")' computes the upper tail probability of
     the Student's T distribution with DF degrees of freedom, at the
     values in X.

     See also: tinv, tpdf, trnd, tstat.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Student's T cumulative distribution function (cdf).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
tinv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 272
 -- tinv (X, N)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the t (Student) distribution with N degrees of
     freedom.

     This function is analogous to looking in a table for the t-value of
     a single-tailed distribution.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
tpdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 164
 -- tpdf (X, N)
     For each element of X, compute the probability density function
     (PDF) at X of the T (Student) distribution with N degrees of
     freedom.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the probability density function (PDF) at
X of...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
tricdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 177
 -- tricdf (X, A, B, C)
     Compute the cumulative distribution function (CDF) at X of the
     triangular distribution with parameters A, B, and C on the interval
     [A, B].


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the cumulative distribution function (CDF) at X of the
triangular dis...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
triinv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
 -- triinv (X, A, B, C)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the triangular distribution with parameters A, B, and
     C on the interval [A, B].


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
tripdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
 -- tripdf (X, A, B, C)
     Compute the probability density function (PDF) at X of the
     triangular distribution with parameters A, B, and C on the interval
     [A, B].


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the probability density function (PDF) at X of the triangular
distrib...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
trirnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 701
 -- trirnd (A, B, C)
 -- trirnd (A, B, C, R)
 -- trirnd (A, B, C, R, C, ...)
 -- trirnd (A, B, C, [SZ])
     Return a matrix of random samples from the rectangular distribution
     with parameters A, B, and C on the interval [A, B].

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of A, B and C.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return a matrix of random samples from the rectangular distribution with
para...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
trnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 628
 -- trnd (N)
 -- trnd (N, R)
 -- trnd (N, R, C, ...)
 -- trnd (N, [SZ])
     Return a matrix of random samples from the t (Student) distribution
     with N degrees of freedom.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the size
     of N.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return a matrix of random samples from the t (Student) distribution with
N de...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
unidcdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
 -- unidcdf (X, N)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of a discrete uniform distribution which assumes the
     integer values 1-N with equal probability.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the cumulative distribution function
(CDF) at ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
unidinv


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
 -- unidinv (X, N)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the discrete uniform distribution which assumes the
     integer values 1-N with equal probability.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
unidpdf


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 -- unidpdf (X, N)
     For each element of X, compute the probability density function
     (PDF) at X of a discrete uniform distribution which assumes the
     integer values 1-N with equal probability.

     Warning: The underlying implementation uses the double class and
     will only be accurate for N < 'flintmax' (2^{53} on IEEE 754
     compatible systems).


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For each element of X, compute the probability density function (PDF) at
X of...



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unidrnd


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 -- unidrnd (N)
 -- unidrnd (N, R)
 -- unidrnd (N, R, C, ...)
 -- unidrnd (N, [SZ])
     Return a matrix of random samples from the discrete uniform
     distribution which assumes the integer values 1-N with equal
     probability.

     N may be a scalar or a multi-dimensional array.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the size
     of N.


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Return a matrix of random samples from the discrete uniform distribution
whic...



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unifcdf


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 -- unifcdf (X)
 -- unifcdf (X, A, B)
     For each element of X, compute the cumulative distribution function
     (CDF) at X of the uniform distribution on the interval [A, B].

     Default values are A = 0, B = 1.


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For each element of X, compute the cumulative distribution function
(CDF) at ...



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unifinv


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 -- unifinv (X)
 -- unifinv (X, A, B)
     For each element of X, compute the quantile (the inverse of the
     CDF) at X of the uniform distribution on the interval [A, B].

     Default values are A = 0, B = 1.


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For each element of X, compute the quantile (the inverse of the CDF) at
X of ...



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unifpdf


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 -- unifpdf (X)
 -- unifpdf (X, A, B)
     For each element of X, compute the probability density function
     (PDF) at X of the uniform distribution on the interval [A, B].

     Default values are A = 0, B = 1.


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For each element of X, compute the probability density function (PDF) at
X of...



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unifrnd


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 -- unifrnd (A, B)
 -- unifrnd (A, B, R)
 -- unifrnd (A, B, R, C, ...)
 -- unifrnd (A, B, [SZ])
     Return a matrix of random samples from the uniform distribution on
     [A, B].

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of A and B.


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Return a matrix of random samples from the uniform distribution on [A,
B].



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vmpdf


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 -- Function File: THETA = vmpdf (X, MU, K)
     Evaluates the Von Mises probability density function.

     The Von Mises distribution has probability density function
          f (X) = exp (K * cos (X - MU)) / Z ,
     where Z is a normalisation constant.  By default, MU is 0 and K is
     1.

     See also: vmrnd.


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Evaluates the Von Mises probability density function.



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vmrnd


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 -- Function File: THETA = vmrnd (MU, K)
 -- Function File: THETA = vmrnd (MU, K, SZ)
     Draw random angles from a Von Mises distribution with mean MU and
     concentration K.

     The Von Mises distribution has probability density function
          f (X) = exp (K * cos (X - MU)) / Z ,
     where Z is a normalisation constant.

     The output, THETA, is a matrix of size SZ containing random angles
     drawn from the given Von Mises distribution.  By default, MU is 0
     and K is 1.

     See also: vmpdf.


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Draw random angles from a Von Mises distribution with mean MU and
concentrati...



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wblcdf


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 -- wblcdf (X)
 -- wblcdf (X, SCALE)
 -- wblcdf (X, SCALE, SHAPE)
     Compute the cumulative distribution function (CDF) at X of the
     Weibull distribution with scale parameter SCALE and shape parameter
     SHAPE.

     This is defined as

          1 - exp (-(x/scale)^shape)

     for X >= 0.

     Default values are SCALE = 1, SHAPE = 1.


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Compute the cumulative distribution function (CDF) at X of the Weibull
distri...



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wblinv


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 -- wblinv (X)
 -- wblinv (X, SCALE)
 -- wblinv (X, SCALE, SHAPE)
     Compute the quantile (the inverse of the CDF) at X of the Weibull
     distribution with scale parameter SCALE and shape parameter SHAPE.

     Default values are SCALE = 1, SHAPE = 1.


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Compute the quantile (the inverse of the CDF) at X of the Weibull
distributio...



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wblpdf


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 -- wblpdf (X)
 -- wblpdf (X, SCALE)
 -- wblpdf (X, SCALE, SHAPE)
     Compute the probability density function (PDF) at X of the Weibull
     distribution with scale parameter SCALE and shape parameter SHAPE.

     This is given by

          shape * scale^(-shape) * x^(shape-1) * exp (-(x/scale)^shape)

     for X >= 0.

     Default values are SCALE = 1, SHAPE = 1.


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Compute the probability density function (PDF) at X of the Weibull
distributi...



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wblrnd


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 -- wblrnd (SCALE, SHAPE)
 -- wblrnd (SCALE, SHAPE, R)
 -- wblrnd (SCALE, SHAPE, R, C, ...)
 -- wblrnd (SCALE, SHAPE, [SZ])
     Return a matrix of random samples from the Weibull distribution
     with parameters SCALE and SHAPE.

     When called with a single size argument, return a square matrix
     with the dimension specified.  When called with more than one
     scalar argument the first two arguments are taken as the number of
     rows and columns and any further arguments specify additional
     matrix dimensions.  The size may also be specified with a vector of
     dimensions SZ.

     If no size arguments are given then the result matrix is the common
     size of SCALE and SHAPE.


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Return a matrix of random samples from the Weibull distribution with
paramete...



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wienrnd


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 -- wienrnd (T, D, N)
     Return a simulated realization of the D-dimensional Wiener Process
     on the interval [0, T].

     If D is omitted, D = 1 is used.  The first column of the return
     matrix contains time, the remaining columns contain the Wiener
     process.

     The optional parameter N defines the number of summands used for
     simulating the process over an interval of length 1.  If N is
     omitted, N = 1000 is used.


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Return a simulated realization of the D-dimensional Wiener Process on
the int...



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wishpdf


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 -- Function File: Y = wishpdf (W, SIGMA, DF, LOG_Y=false)
     Compute the probability density function of the Wishart
     distribution

     Inputs: A P x P matrix W where to find the PDF. The P x P positive
     definite matrix SIGMA and scalar degrees of freedom parameter DF
     characterizing the Wishart distribution.  (For the density to be
     finite, need DF > (P - 1).)

     If the flag LOG_Y is set, return the log probability density - this
     helps avoid underflow when the numerical value of the density is
     very small

     Output: Y is the probability density of Wishart(SIGMA, DF) at W.

     See also: wishrnd, iwishpdf.


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Compute the probability density function of the Wishart distribution



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wishrnd


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 -- Function File: [W[, D]] = wishrnd (SIGMA, DF[, D][, N=1])
     Return a random matrix sampled from the Wishart distribution with
     given parameters

     Inputs: the P x P positive definite matrix SIGMA (or the
     lower-triangular Cholesky factor D of SIGMA) and scalar degrees of
     freedom parameter DF.

     DF can be non-integer as long as DF > P

     Output: a random P x P matrix W from the Wishart(SIGMA, DF)
     distribution.  If N > 1, then W is P x P x N and holds N such
     random matrices.  (Optionally, the lower-triangular Cholesky factor
     D of SIGMA is also returned.)

     Averaged across many samples, the mean of W should approach
     DF*SIGMA, and the variance of each element W_ij should approach
     DF*(SIGMA_ij^2 + SIGMA_ii*SIGMA_jj)

     Reference: Yu-Cheng Ku and Peter Bloomfield (2010), Generating
     Random Wishart Matrices with Fractional Degrees of Freedom in OX,
     http://www.gwu.edu/~forcpgm/YuChengKu-030510final-WishartYu-ChengKu.pdf

     See also: iwishrnd, wishpdf.


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Return a random matrix sampled from the Wishart distribution with given
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