Gamma (OpenGamma Strata Math API)

java.lang.Object
- com.opengamma.strata.math.impl.cern.Gamma

All Implemented Interfaces:

Serializable, Cloneable, DoubleUnaryOperator, IntUnaryOperator
```
public class Gamma
extends Object
```
Gamma distribution; math definition, definition of gamma function and animated definition.
p(x) = k * x^(alpha-1) * e^(-x/beta) with k = 1/(g(alpha) * b^a)) and g(a) being the gamma function.
Valid parameter ranges: alpha > 0.
Note: For a Gamma distribution to have the mean mean and variance variance, set the parameters as follows:
```
 alpha = mean*mean / variance; lambda = 1 / (variance / mean); 
 
```
Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.
Static methods operate on a default uniform random number generator; they are synchronized.
Implementation:
Method: Acceptance Rejection combined with Acceptance Complement.
High performance implementation. This is a port of RandGamma used in CLHEP 1.4.0 (C++). CLHEP's implementation, in turn, is based on gds.c from the C-RAND / WIN-RAND library. C-RAND's implementation, in turn, is based upon
J.H. Ahrens, U. Dieter (1974): Computer methods for sampling from gamma, beta, Poisson and binomial distributions, Computing 12, 223-246.
and
J.H. Ahrens, U. Dieter (1982): Generating gamma variates by a modified rejection technique, Communications of the ACM 25, 47-54.
Version:

1.0, 09/24/99

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

protected double alpha

protected double lambda

protected RandomEngine randomGenerator

protected static Gamma shared

Fields
Modifier and Type	Field and Description
`protected double`	`alpha`
`protected double`	`lambda`
`protected RandomEngine`	`randomGenerator`
`protected static Gamma`	`shared`

Constructor Summary

Constructors
Constructor and Description

Gamma(double alpha, double lambda, RandomEngine randomGenerator)
Constructs a Gamma distribution.

Constructors
Constructor and Description
`Gamma(double alpha, double lambda, RandomEngine randomGenerator)` Constructs a Gamma distribution.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`applyAsDouble(double dummy)` Equivalent to `nextDouble()`.
`int`	`applyAsInt(int dummy)` Equivalent to `nextInt()`.
`double`	`cdf(double x)` Returns the cumulative distribution function.
`Object`	`clone()` Returns a deep copy of the receiver; the copy will produce identical sequences.
`protected RandomEngine`	`getRandomGenerator()` Returns the used uniform random number generator;
`static RandomEngine`	`makeDefaultGenerator()` Constructs and returns a new uniform random number generation engine seeded with the current time.
`double`	`nextDouble()` Returns a random number from the distribution.
`double`	`nextDouble(double alpha, double lambda)` Returns a random number from the distribution; bypasses the internal state.
`int`	`nextInt()` Returns a random number from the distribution; returns `(int) Math.round(nextDouble())`.
`double`	`pdf(double x)` Returns the probability distribution function.
`protected void`	`setRandomGenerator(RandomEngine randomGenerator)` Sets the uniform random generator internally used.
`void`	`setState(double alpha, double lambda)` Sets the mean and variance.
`static double`	`staticNextDouble(double alpha, double lambda)` Returns a random number from the distribution.
`String`	`toString()` Returns a String representation of the receiver.

Methods inherited from class java.lang.Object
equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.util.function.DoubleUnaryOperator
andThen, compose, identity

Methods inherited from interface java.util.function.IntUnaryOperator
andThen, compose, identity

- Field Detail
  - alpha
```
protected double alpha
```
  - lambda
```
protected double lambda
```
  - shared
```
protected static Gamma shared
```
  - randomGenerator
```
protected RandomEngine randomGenerator
```
- Constructor Detail
  - Gamma
```
public Gamma(double alpha,
             double lambda,
             RandomEngine randomGenerator)
```
    Constructs a Gamma distribution. Example: alpha=1.0, lambda=1.0.
    
    Parameters:
    
    alpha - alpha
    
    lambda - lambda
    
    randomGenerator - generator
    
    Throws:
    
    IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.
- Method Detail
  - cdf
```
public double cdf(double x)
```
    Returns the cumulative distribution function.
    
    Parameters:
    
    x - x
    
    Returns:
    
    result
  - nextDouble
```
public double nextDouble()
```
    Returns a random number from the distribution.
    
    Returns:
    
    result
  - nextDouble
```
public double nextDouble(double alpha,
                         double lambda)
```
    Returns a random number from the distribution; bypasses the internal state.
    
    Parameters:
    
    alpha - alpha
    
    lambda - lambda
    
    Returns:
    
    result
  - pdf
```
public double pdf(double x)
```
    Returns the probability distribution function.
    
    Parameters:
    
    x - x
    
    Returns:
    
    result
  - setState
```
public void setState(double alpha,
                     double lambda)
```
    Sets the mean and variance.
    
    Parameters:
    
    alpha - alpha
    
    lambda - lambda
    
    Throws:
    
    IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.
  - staticNextDouble
```
public static double staticNextDouble(double alpha,
                                      double lambda)
```
    Returns a random number from the distribution.
    
    Parameters:
    
    alpha - alpha
    
    lambda - lambda
    
    Returns:
    
    result
    
    Throws:
    
    IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.
  - toString
```
public String toString()
```
    Returns a String representation of the receiver.
    
    Overrides:
    
    toString in class Object
  - applyAsDouble
```
public double applyAsDouble(double dummy)
```
    Equivalent to nextDouble(). This has the effect that distributions can now be used as function objects, returning a random number upon function evaluation.
    
    Specified by:
    
    applyAsDouble in interface DoubleUnaryOperator
  - applyAsInt
```
public int applyAsInt(int dummy)
```
    Equivalent to nextInt(). This has the effect that distributions can now be used as function objects, returning a random number upon function evaluation.
    
    Specified by:
    
    applyAsInt in interface IntUnaryOperator
  - clone
```
public Object clone()
```
    Returns a deep copy of the receiver; the copy will produce identical sequences. After this call has returned, the copy and the receiver have equal but separate state.
    
    Returns:
    
    a copy of the receiver.
  - getRandomGenerator
```
protected RandomEngine getRandomGenerator()
```
    Returns the used uniform random number generator;
    
    Returns:
    
    result
  - makeDefaultGenerator
```
public static RandomEngine makeDefaultGenerator()
```
    Constructs and returns a new uniform random number generation engine seeded with the current time. Currently this is MersenneTwister.
    
    Returns:
    
    result
  - nextInt
```
public int nextInt()
```
    Returns a random number from the distribution; returns (int) Math.round(nextDouble()). Override this method if necessary.
    
    Returns:
    
    result
  - setRandomGenerator
```
protected void setRandomGenerator(RandomEngine randomGenerator)
```
    Sets the uniform random generator internally used.
    
    Parameters:
    
    randomGenerator - input

Copyright 2009-Present by OpenGamma Inc. and individual contributors
Apache v2 licensed
Additional documentation can be found at strata.opengamma.io.

Class Gamma

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface java.util.function.DoubleUnaryOperator

Methods inherited from interface java.util.function.IntUnaryOperator

Field Detail

alpha

lambda

shared

randomGenerator

Constructor Detail

Gamma

Method Detail

cdf

nextDouble

nextDouble

pdf

setState

staticNextDouble

toString

applyAsDouble

applyAsInt

clone

getRandomGenerator

makeDefaultGenerator

nextInt

setRandomGenerator