## 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

Actions | Description |
---|---|

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)
```

#### Parameters

- Libraries.Language.Object: The object to compare to.

#### 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

- Libraries.Language.Object: The to be compared.

#### Return

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

### Gamma(number x)

#### 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)

#### 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)

#### Parameters

#### Return

number