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## sim.util.distribution
Class Gamma

    java.lang.Object
      sim.util.distribution.AbstractDistribution
          sim.util.distribution.AbstractContinousDistribution
              sim.util.distribution.Gamma

All Implemented Interfaces:
  java.io.Serializable

    public class Gamma

extends AbstractContinousDistribution

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.

See Also:
  Serialized Form

Field Summary
`protected double` | `alpha`
`protected double` | `lambda`

Fields inherited from class sim.util.distribution.AbstractDistribution
`randomGenerator`

Constructor Summary
`Gamma(double alpha, double lambda, MersenneTwisterFast randomGenerator)` Constructs a Gamma distribution.

Method Summary
`double` | `cdf(double x)` Returns the cumulative distribution function.
`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.
`double` | `pdf(double x)` Returns the probability distribution function.
`void` | `setState(double alpha, double lambda)` Sets the mean and variance.
`java.lang.String` | `toString()` Returns a String representation of the receiver.

Methods inherited from class sim.util.distribution.AbstractDistribution
`apply, apply, getRandomGenerator, nextInt, setRandomGenerator`

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

Field Detail

### alpha

    protected double alpha

### lambda

    protected double lambda

Constructor Detail

### Gamma

    public Gamma(double alpha,
                 double lambda,
                 MersenneTwisterFast randomGenerator)

  Constructs a Gamma distribution. Example: alpha=1.0, lambda=1.0.

  Throws:
    `java.lang.IllegalArgumentException` - if `alpha <= 0.0 || lambda <= 0.0`.

Method Detail

### cdf

    public double cdf(double x)

  Returns the cumulative distribution function.

### nextDouble

    public double nextDouble()

  Returns a random number from the distribution.

  Specified by:
    `nextDouble` in class `AbstractDistribution`

### nextDouble

    public double nextDouble(double alpha,
                             double lambda)

  Returns a random number from the distribution; bypasses the internal state.

### pdf

    public double pdf(double x)

  Returns the probability distribution function.

### setState

    public void setState(double alpha,
                         double lambda)

  Sets the mean and variance.

  Throws:
    `java.lang.IllegalArgumentException` - if `alpha <= 0.0 || lambda <= 0.0`.

### toString

    public java.lang.String toString()

  Returns a String representation of the receiver.

  Overrides:
    `toString` in class `java.lang.Object`

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