## 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

### 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)
GetHashCode()This action gets the hash code for an object.
InvGamma1pm1(number x)
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)

## 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.

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.

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)

#### Return

number