Distributions
cern.jet.random

Class Distributions



  • public class Distributionsextends Object
    Contains methods for conveniently generating pseudo-random numbers from special distributions such as the Burr, Cauchy, Erlang, Geometric, Lambda, Laplace, Logistic, Weibull, etc.

    About this class:

    All distributions are obtained by using a uniform pseudo-random number generator. followed by a transformation to the desired distribution.

    Example usage:

     cern.jet.random.engine.RandomEngine generator; generator = new cern.jet.random.engine.MersenneTwister(new java.util.Date()); //generator = new edu.cornell.lassp.houle.RngPack.Ranecu(new java.util.Date()); //generator = new edu.cornell.lassp.houle.RngPack.Ranmar(new java.util.Date()); //generator = new edu.cornell.lassp.houle.RngPack.Ranlux(new java.util.Date()); //generator = AbstractDistribution.makeDefaultGenerator(); for (int i=1000000; --i >=0; ) {    int cauchy = Distributions.nextCauchy(generator);    ... } 
    See Also:
    MersenneTwister, Random, Math
    • Method Summary

      Methods 
      Modifier and TypeMethod and Description
      static doublegeometricPdf(int k, double p)
      Returns the probability distribution function of the discrete geometric distribution.
      static doublenextBurr1(double r, int nr, RandomEngine randomGenerator)
      Returns a random number from the Burr II, VII, VIII, X Distributions.
      static doublenextBurr2(double r, double k, int nr, RandomEngine randomGenerator)
      Returns a random number from the Burr III, IV, V, VI, IX, XII distributions.
      static doublenextCauchy(RandomEngine randomGenerator)
      Returns a cauchy distributed random number from the standard Cauchy distribution C(0,1).
      static doublenextErlang(double variance, double mean, RandomEngine randomGenerator)
      Returns an erlang distributed random number with the given variance and mean.
      static intnextGeometric(double p, RandomEngine randomGenerator)
      Returns a discrete geometric distributed random number; Definition.
      static doublenextLambda(double l3, double l4, RandomEngine randomGenerator)
      Returns a lambda distributed random number with parameters l3 and l4.
      static doublenextLaplace(RandomEngine randomGenerator)
      Returns a Laplace (Double Exponential) distributed random number from the standard Laplace distribution L(0,1).
      static doublenextLogistic(RandomEngine randomGenerator)
      Returns a random number from the standard Logistic distribution Log(0,1).
      static doublenextPowLaw(double alpha, double cut, RandomEngine randomGenerator)
      Returns a power-law distributed random number with the given exponent and lower cutoff.
      static doublenextTriangular(RandomEngine randomGenerator)
      Returns a random number from the standard Triangular distribution in (-1,1).
      static doublenextWeibull(double alpha, double beta, RandomEngine randomGenerator)
      Returns a weibull distributed random number.
      static intnextZipfInt(double z, RandomEngine randomGenerator)
      Returns a zipfian distributed random number with the given skew.
    • Method Detail

      • geometricPdf

        public static double geometricPdf(int k,                  double p)
        Returns the probability distribution function of the discrete geometric distribution.

        p(k) = p * (1-p)^k for k >= 0.

        Parameters:
        k - the argument to the probability distribution function.
        p - the parameter of the probability distribution function.
      • nextBurr1

        public static double nextBurr1(double r,               int nr,               RandomEngine randomGenerator)
        Returns a random number from the Burr II, VII, VIII, X Distributions.

        Implementation: Inversion method. This is a port of burr1.c from the C-RAND / WIN-RAND library. C-RAND's implementation, in turn, is based upon

        L. Devroye (1986): Non-Uniform Random Variate Generation, Springer Verlag, New York.

        Parameters:
        r - must be > 0.
        nr - the number of the burr distribution (e.g. 2,7,8,10).
      • nextBurr2

        public static double nextBurr2(double r,               double k,               int nr,               RandomEngine randomGenerator)
        Returns a random number from the Burr III, IV, V, VI, IX, XII distributions.

        Implementation: Inversion method. This is a port of burr2.c from the C-RAND / WIN-RAND library. C-RAND's implementation, in turn, is based upon

        L. Devroye (1986): Non-Uniform Random Variate Generation, Springer Verlag, New York.

        Parameters:
        r - must be > 0.
        k - must be > 0.
        nr - the number of the burr distribution (e.g. 3,4,5,6,9,12).
      • nextErlang

        public static double nextErlang(double variance,                double mean,                RandomEngine randomGenerator)
        Returns an erlang distributed random number with the given variance and mean.
      • nextGeometric

        public static int nextGeometric(double p,                RandomEngine randomGenerator)
        Returns a discrete geometric distributed random number; Definition.

        p(k) = p * (1-p)^k for k >= 0.

        Implementation: Inversion method. This is a port of geo.c from the C-RAND / WIN-RAND library.

        Parameters:
        p - must satisfy 0 < p < 1.

      • nextLambda

        public static double nextLambda(double l3,                double l4,                RandomEngine randomGenerator)
        Returns a lambda distributed random number with parameters l3 and l4.

        Implementation: Inversion method. This is a port of lamin.c from the C-RAND / WIN-RAND library. C-RAND's implementation, in turn, is based upon

        J.S. Ramberg, B:W. Schmeiser (1974): An approximate method for generating asymmetric variables, Communications ACM 17, 78-82.

      • nextLaplace

        public static double nextLaplace(RandomEngine randomGenerator)
        Returns a Laplace (Double Exponential) distributed random number from the standard Laplace distribution L(0,1).

        Implementation: Inversion method. This is a port of lapin.c from the C-RAND / WIN-RAND library.

      • nextLogistic

        public static double nextLogistic(RandomEngine randomGenerator)
        Returns a random number from the standard Logistic distribution Log(0,1).

        Implementation: Inversion method. This is a port of login.c from the C-RAND / WIN-RAND library.

      • nextPowLaw

        public static double nextPowLaw(double alpha,                double cut,                RandomEngine randomGenerator)
        Returns a power-law distributed random number with the given exponent and lower cutoff.
        Parameters:
        alpha - the exponent
        cut - the lower cutoff
      • nextTriangular

        public static double nextTriangular(RandomEngine randomGenerator)
        Returns a random number from the standard Triangular distribution in (-1,1).

        Implementation: Inversion method. This is a port of tra.c from the C-RAND / WIN-RAND library.

      • nextWeibull

        public static double nextWeibull(double alpha,                 double beta,                 RandomEngine randomGenerator)
        Returns a weibull distributed random number. Polar method. See Simulation, Modelling & Analysis by Law & Kelton, pp259
      • nextZipfInt

        public static int nextZipfInt(double z,              RandomEngine randomGenerator)
        Returns a zipfian distributed random number with the given skew.

        Algorithm from page 551 of: Devroye, Luc (1986) `Non-uniform random variate generation', Springer-Verlag: Berlin. ISBN 3-540-96305-7 (also 0-387-96305-7)

        Parameters:
        z - the skew of the distribution (must be >1.0).

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