Package org.apache.commons.statistics.inference

Class StatisticUtils

java.lang.Object

org.apache.commons.statistics.inference.StatisticUtils

final class StatisticUtils
extends java.lang.Object

Utility computation methods.

Since:

1.1

Constructor Summary

Constructors

Modifier	Constructor	Description
private	StatisticUtils()	No instances.

Method Summary

Modifier and Type	Method	Description
private static org.apache.commons.numbers.core.DD	add(org.apache.commons.numbers.core.DD sum, long v)	Adds the value to the sum.
(package private) static int	computeDegreesOfFreedom(int n, int m)	Compute the degrees of freedom as n - 1 - m.
(package private) static double	computeRatio(double[] expected, long[] observed)	Gets the ratio between the sum of the observed and expected values.
(package private) static double	mean(java.util.Collection<double[]> samples)	Returns the arithmetic mean of the entries in the input arrays, or NaN if the combined length of the arrays is zero.
(package private) static double	meanDifference(double[] x, double[] y)	Returns the mean of the (signed) differences between corresponding elements of the input arrays.
(package private) static double[]	subtract(double[] x, double y)	Compute x - y.
(package private) static double	varianceDifference(double[] x, double[] y, double mean)	Returns the variance of the (signed) differences between corresponding elements of the input arrays, or NaN if the arrays are empty.

Methods inherited from class java.lang.Object

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

Constructor Detail

StatisticUtils

private StatisticUtils()

No instances.

Method Detail

subtract

static double[] subtract(double[] x,
                         double y)

Compute x - y.

If y is zero the original array is returned, else a new array is created with the difference.

Parameters:

x - Array.

y - Value.

Returns:

x - y

Throws:

java.lang.NullPointerException - if x is null and y is non-zero

computeDegreesOfFreedom

static int computeDegreesOfFreedom(int n,
                                   int m)

Compute the degrees of freedom as n - 1 - m.

This method is common functionality shared between the Chi-square test and G-test. The pre-conditions for those tests are performed by this method.

Parameters:

n - Number of observations.

m - Adjustment (assumed to be positive).

Returns:

the degrees of freedom

Throws:

java.lang.IllegalArgumentException - if the degrees of freedom is not strictly positive

computeRatio

static double computeRatio(double[] expected,
                           long[] observed)

Gets the ratio between the sum of the observed and expected values. The ratio can be used to scale the expected values to have the same sum as the observed values:

 sum(o) = sum(e * ratio)
 

This method is common functionality shared between the Chi-square test and G-test. The pre-conditions for those tests are performed by this method.

Parameters:

expected - Expected values.

observed - Observed values.

Returns:

the ratio

Throws:

java.lang.IllegalArgumentException - if the sample size is less than 2; the array sizes do not match; expected has entries that are not strictly positive; observed has negative entries; or all the observations are zero.

add

private static org.apache.commons.numbers.core.DD add(org.apache.commons.numbers.core.DD sum,
                                                      long v)

Adds the value to the sum.

Parameters:

sum - Sum.

v - Value.

Returns:

the new sum

mean

static double mean(java.util.Collection<double[]> samples)

Returns the arithmetic mean of the entries in the input arrays, or NaN if the combined length of the arrays is zero.

Supports a combined length above the maximum array size.

A two-pass, corrected algorithm is used, starting with the definitional formula computed using the array of stored values and then correcting this by adding the mean deviation of the data values from the arithmetic mean. See, e.g. "Comparison of Several Algorithms for Computing Sample Means and Variances," Robert F. Ling, Journal of the American Statistical Association, Vol. 69, No. 348 (Dec., 1974), pp. 859-866.

Parameters:

samples - Values.

Returns:

the mean of the values or NaN if length = 0

meanDifference

static double meanDifference(double[] x,
                             double[] y)

Returns the mean of the (signed) differences between corresponding elements of the input arrays.

 sum(x[i] - y[i]) / x.length
 

This method avoids intermediate array allocation.

Parameters:

x - First array.

y - Second array.

Returns:

mean of paired differences

Throws:

java.lang.IllegalArgumentException - if the arrays do not have the same length.

varianceDifference

static double varianceDifference(double[] x,
                                 double[] y,
                                 double mean)

Returns the variance of the (signed) differences between corresponding elements of the input arrays, or NaN if the arrays are empty.

 var(x[i] - y[i])
 

Returns the bias-corrected sample variance (using n - 1 in the denominator). Returns 0 for a single-value (i.e. length = 1) sample.

This method avoids intermediate array allocation.

Uses a two-pass algorithm. Specifically, these methods use the "corrected two-pass algorithm" from Chan, Golub, Levesque, Algorithms for Computing the Sample Variance, American Statistician, vol. 37, no. 3 (1983) pp. 242-247.

Parameters:

x - First array.

y - Second array.

mean - the mean difference between corresponding entries

Returns:

variance of paired differences

Throws:

java.lang.IllegalArgumentException - if the arrays do not have the same length.

See Also:

meanDifference(double[], double[])