Class Binomial

java.lang.Object
cern.colt.PersistentObject
cern.jet.random.AbstractDistribution
cern.jet.random.AbstractDiscreteDistribution
cern.jet.random.Binomial
All Implemented Interfaces:
DoubleFunction, IntFunction, Serializable, Cloneable
public class Binomial extends AbstractDiscreteDistribution
Binomial distribution; See the math definition and animated definition.

p(x) = k * p^k * (1-p)^(n-k) with k = n! / (k! * (n-k)!).

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Implementation: High performance implementation. Acceptance Rejection/Inversion method. This is a port of RandBinomial used in CLHEP 1.4.0 (C++). CLHEP's implementation is, in turn, based on

V. Kachitvichyanukul, B.W. Schmeiser (1988): Binomial random variate generation, Communications of the ACM 31, 216-222.

Version:
1.0, 09/24/99
See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private int
    b
     
    private double
    c
     
    private double
    ch
     
    private double
    ll
     
    private double
    log_n
     
    private double
    log_p
     
    private double
    log_q
     
    private double
    lr
     
    private int
    m
     
    protected int
    n
     
    private int
    n_last
     
    private int
    n_prev
     
    private int
    nm
     
    private double
    np
     
    protected double
    p
     
    private double
    p_last
     
    private double
    p_prev
     
    private double
    p0
     
    private double
    p1
     
    private double
    p2
     
    private double
    p3
     
    private double
    p4
     
    private double
    par
     
    private double
    pq
     
    private double
    q
     
    private double
    rc
     
    protected static Binomial
    shared
     
    private double
    ss
     
    private double
    xl
     
    private double
    xm
     
    private double
    xr
     

    Fields inherited from class AbstractDistribution

    randomGenerator

    Fields inherited from class PersistentObject

    serialVersionUID

  • Constructor Summary

    Constructors
    Constructor
    Description
    Binomial(int n, double p, RandomEngine randomGenerator)
    Constructs a binomial distribution.

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cdf(int k)
    Returns the cumulative distribution function.
    private double
    cdfSlow(int k)
    Returns the cumulative distribution function.
    protected int
    generateBinomial(int n, double p)
    * Binomial-Distribution - Acceptance Rejection/Inversion * * * Acceptance Rejection method combined with Inversion for * generating Binomial random numbers with parameters * n (number of trials) and p (probability of success).
    int
    nextInt()
    Returns a random number from the distribution.
    int
    nextInt(int n, double p)
    Returns a random number from the distribution with the given parameters n and p; bypasses the internal state.
    double
    pdf(int k)
    Returns the probability distribution function.
    void
    setNandP(int n, double p)
    Sets the parameters number of trials and the probability of success.
    static int
    staticNextInt(int n, double p)
    Returns a random number from the distribution with the given parameters n and p.
    String
    toString()
    Returns a String representation of the receiver.
    private static void
    xstaticSetRandomGenerator(RandomEngine randomGenerator)
    Sets the uniform random number generated shared by all static methods.

    Methods inherited from class AbstractDiscreteDistribution

    nextDouble

    Methods inherited from class AbstractDistribution

    apply, apply, clone, getRandomGenerator, makeDefaultGenerator, setRandomGenerator

    Methods inherited from class Object

    equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

  • Field Details

    • n

      protected int n

    • p

      protected double p

    • n_last

      private int n_last

    • n_prev

      private int n_prev

    • par

      private double par

    • np

      private double np

    • p0

      private double p0

    • q

      private double q

    • p_last

      private double p_last

    • p_prev

      private double p_prev

    • b

      private int b

    • m

      private int m

    • nm

      private int nm

    • pq

      private double pq

    • rc

      private double rc

    • ss

      private double ss

    • xm

      private double xm

    • xl

      private double xl

    • xr

      private double xr

    • ll

      private double ll

    • lr

      private double lr

    • c

      private double c

    • p1

      private double p1

    • p2

      private double p2

    • p3

      private double p3

    • p4

      private double p4

    • ch

      private double ch

    • log_p

      private double log_p

    • log_q

      private double log_q

    • log_n

      private double log_n

    • shared

      protected static Binomial shared

  • Constructor Details

    • Binomial

      public Binomial(int n, double p, RandomEngine randomGenerator)
      Constructs a binomial distribution. Example: n=1, p=0.5.
      Parameters:
      n - the number of trials (also known as sample size).
      p - the probability of success.
      randomGenerator - a uniform random number generator.
      Throws:
      IllegalArgumentException - if n*Math.min(p,1-p) <= 0.0

  • Method Details

    • cdf

      public double cdf(int k)
      Returns the cumulative distribution function.

    • cdfSlow

      private double cdfSlow(int k)
      Returns the cumulative distribution function.

    • generateBinomial

      protected int generateBinomial(int n, double p)
      * Binomial-Distribution - Acceptance Rejection/Inversion * * * Acceptance Rejection method combined with Inversion for * generating Binomial random numbers with parameters * n (number of trials) and p (probability of success). * For min(n*p,n*(1-p)) invalid input: '<' 10 the Inversion method is applied: * The random numbers are generated via sequential search, * starting at the lowest index k=0. The cumulative probabilities * are avoided by using the technique of chop-down. * For min(n*p,n*(1-p)) >= 10 Acceptance Rejection is used: * The algorithm is based on a hat-function which is uniform in * the centre region and exponential in the tails. * A triangular immediate acceptance region in the centre speeds * up the generation of binomial variates. * If candidate k is near the mode, f(k) is computed recursively * starting at the mode m. * The acceptance test by Stirling's formula is modified * according to W. Hoermann (1992): The generation of binomial * random variates, to appear in J. Statist. Comput. Simul. * If p invalid input: '<' .5 the algorithm is applied to parameters n, p. * Otherwise p is replaced by 1-p, and k is replaced by n - k. * * * FUNCTION: - samples a random number from the binomial * distribution with parameters n and p and is * valid for n*min(p,1-p) > 0. * REFERENCE: - V. Kachitvichyanukul, B.W. Schmeiser (1988): * Binomial random variate generation, * Communications of the ACM 31, 216-222. * SUBPROGRAMS: - StirlingCorrection() * ... Correction term of the Stirling * approximation for log(k!) * (series in 1/k or table values * for small k) with long int k * - randomGenerator ... (0,1)-Uniform engine * *

    • nextInt

      public int nextInt()
      Returns a random number from the distribution.
      Specified by:
      nextInt in class AbstractDiscreteDistribution

    • nextInt

      public int nextInt(int n, double p)
      Returns a random number from the distribution with the given parameters n and p; bypasses the internal state.
      Parameters:
      n - the number of trials
      p - the probability of success.
      Throws:
      IllegalArgumentException - if n*Math.min(p,1-p) <= 0.0

    • pdf

      public double pdf(int k)
      Returns the probability distribution function.

    • setNandP

      public void setNandP(int n, double p)
      Sets the parameters number of trials and the probability of success.
      Parameters:
      n - the number of trials
      p - the probability of success.
      Throws:
      IllegalArgumentException - if n*Math.min(p,1-p) <= 0.0

    • staticNextInt

      public static int staticNextInt(int n, double p)
      Returns a random number from the distribution with the given parameters n and p.
      Parameters:
      n - the number of trials
      p - the probability of success.
      Throws:
      IllegalArgumentException - if n*Math.min(p,1-p) <= 0.0

    • toString

      public String toString()
      Returns a String representation of the receiver.
      Overrides:
      toString in class Object

    • xstaticSetRandomGenerator

      private static void xstaticSetRandomGenerator(RandomEngine randomGenerator)
      Sets the uniform random number generated shared by all static methods.
      Parameters:
      randomGenerator - the new uniform random number generator to be shared.