## 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)``````

#### 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)``````

#### 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}.

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}.

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.

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)].

#### Return

number:

### LogGamma1p(number x)

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

#### 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

• number a: the a parameter.
• number x: the value.

#### 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

• number a: the a parameter.
• number x: the value.
• number epsilon: When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.
• integer maxIterations: Maximum number of "iterations" to complete.

#### 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

• number a: the a parameter.
• number x: the value.

#### 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

• number a: the a parameter.
• number x: the value.
• number epsilon: When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.
• integer maxIterations: Maximum number of "iterations" to complete.

#### Return

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