Package sim.util.distribution

Class Gamma

java.lang.Object
sim.util.distribution.AbstractDistribution
sim.util.distribution.AbstractContinuousDistribution
sim.util.distribution.Gamma
All Implemented Interfaces:
Serializable
public class Gamma extends AbstractContinuousDistribution
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:

  • Field Details

    • alpha

      protected double alpha

    • lambda

      protected double lambda

  • Constructor Details

    • Gamma

      public Gamma(double alpha, double lambda, MersenneTwisterFast randomGenerator)
      Constructs a Gamma distribution. Example: alpha=1.0, lambda=1.0.
      Throws:
      IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.

  • Method Details

    • 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:
      IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.

    • toString

      public String toString()
      Returns a String representation of the receiver.
      Overrides:
      toString in class Object