Libraries.Compute.Statistics.Distributions.Gamma Documentation

This class, ported from Apache Commons, is an implementation of the Gamma Distribution. More information can be found here: https://en.wikipedia.org/wiki/Gamma_distribution

Inherits from: Libraries.Language.Object

Summary

Variable Summary Table

VariablesDescription
number DEFAULT_EPSILON

Actions Summary Table

ActionsDescription
Compare(Libraries.Language.Object object)This action compares two object hash codes and returns an integer.
Equals(Libraries.Language.Object object)This action determines if two objects are equal based on their hash code values.
Gamma(number x)* The constant {@code C12} defined in {@code DGAM1}.
GetHashCode()This action gets the hash code for an object.
InvGamma1pm1(number x)* The constant {@code C9} defined in {@code DGAM1}.
Lanczos(number x)* From the recurrence relation * Gamma(x) = (x - 1) * .
LogGamma(number x)* From the reflection formula * Gamma(x) * Gamma(1 - x) * sin(pi * x) = pi, * and the recurrence relation * Gamma(1 - x) = -x * Gamma(-x), * it is found * Gamma(x) = -pi / [x * sin(pi * x) * Gamma(-x)].
LogGamma1p(number x)* The constant {@code C10} defined in {@code DGAM1}.
RegularizedGammaP(number a, number x)Returns the regularized gamma function P(a, x).
RegularizedGammaP(number a, number x, number epsilon, integer maxIterations)Returns the regularized gamma function P(a, x).
RegularizedGammaQ(number a, number x)Returns the regularized gamma function Q(a, x) = 1 - P(a, x).
RegularizedGammaQ(number a, number x, number epsilon, integer maxIterations)Returns the regularized gamma function Q(a, x) = 1 - P(a, x).

Actions Documentation

Compare(Libraries.Language.Object object)

This action compares two object hash codes and returns an integer. The result is larger if this hash code is larger than the object passed as a parameter, smaller, or equal. In this case, -1 means smaller, 0 means equal, and 1 means larger. This action was changed in Quorum 7 to return an integer, instead of a CompareResult object, because the previous implementation was causing efficiency issues.

Example Code

Object o
        Object t
        integer result = o:Compare(t) //1 (larger), 0 (equal), or -1 (smaller)

Parameters

Return

integer: The Compare result, Smaller, Equal, or Larger.

Equals(Libraries.Language.Object object)

This action determines if two objects are equal based on their hash code values.

Example Code

use Libraries.Language.Object
        use Libraries.Language.Types.Text
        Object o
        Text t
        boolean result = o:Equals(t)

Parameters

Return

boolean: True if the hash codes are equal and false if they are not equal.

Gamma(number x)

* The constant {@code C12} defined in {@code DGAM1}.

Parameters

Return

number:

GetHashCode()

This action gets the hash code for an object.

Example Code

Object o
        integer hash = o:GetHashCode()

Return

integer: The integer hash code of the object.

InvGamma1pm1(number x)

* The constant {@code C9} defined in {@code DGAM1}.

Parameters

Return

number:

Lanczos(number x)

* From the recurrence relation * Gamma(x) = (x - 1) * ... * (x - n) * Gamma(x - n), * then * Gamma(t) = 1 / [1 + invGamma1pm1(t - 1)], * where t = x - n. This means that t must satisfy * -0.5 <= t - 1 <= 1.5.

Parameters

Return

number:

LogGamma(number x)

* From the reflection formula * Gamma(x) * Gamma(1 - x) * sin(pi * x) = pi, * and the recurrence relation * Gamma(1 - x) = -x * Gamma(-x), * it is found * Gamma(x) = -pi / [x * sin(pi * x) * Gamma(-x)].

Parameters

Return

number:

LogGamma1p(number x)

* The constant {@code C10} defined in {@code DGAM1}.

Parameters

Return

number:

RegularizedGammaP(number a, number x)

Returns the regularized gamma function P(a, x). The action is ported from Apache Commons. This uses the default epsilon (error) and the maximum number of iterations is the largest possible integer.

Parameters

Return

number: the regularized gamma function P(a, x)

RegularizedGammaP(number a, number x, number epsilon, integer maxIterations)

Returns the regularized gamma function P(a, x). The action is ported from Apache Commons The implementation of this method is based on:

Parameters

Return

number: the regularized gamma function P(a, x)

RegularizedGammaQ(number a, number x)

Returns the regularized gamma function Q(a, x) = 1 - P(a, x). This is adapted from Apache Commons.

Parameters

Return

number: the regularized gamma function P(a, x)

RegularizedGammaQ(number a, number x, number epsilon, integer maxIterations)

Returns the regularized gamma function Q(a, x) = 1 - P(a, x). This is adapted from Apache Commons. The implementation of this method is based on:

Parameters

Return

number: the regularized gamma function P(a, x)