Gamma
cern.jet.random

Class Gamma

  • All Implemented Interfaces:
    DoubleFunction, IntFunction, Serializable, Cloneable


    public class Gammaextends 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
    • Constructor Detail

      • Gamma

        public Gamma(double alpha,     double lambda,     RandomEngine randomGenerator)
        Constructs a Gamma distribution. Example: alpha=1.0, lambda=1.0.
        Throws:
        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(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.
      • staticNextDouble

        public static double staticNextDouble(double alpha,                      double lambda)
        Returns a random number from the distribution.
        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

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