Package com.opengamma.strata.math.impl.cern

Class 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 Detail

      • alpha

        protected double alpha

      • lambda

        protected double lambda

      • shared

        protected static Gamma shared

    • 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