sim.util.distribution
Class Distributions

java.lang.Object
  sim.util.distribution.Distributions

All Implemented Interfaces:

java.io.Serializable

public class Distributions
extends java.lang.Object
implements java.io.Serializable

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.MersenneTwisterFast 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:

cern.jet.random.engine.MersenneTwister, Random, Math, Serialized Form

Constructor Summary

protected

Distributions() Makes this class non instantiable, but still let's others inherit from it.

Method Summary

static double	geometricPdf(int k, double p) Returns the probability distribution function of the discrete geometric distribution.
static double	nextBurr1(double r, int nr, MersenneTwisterFast randomGenerator) Returns a random number from the Burr II, VII, VIII, X Distributions.
static double	nextBurr2(double r, double k, int nr, MersenneTwisterFast randomGenerator) Returns a random number from the Burr III, IV, V, VI, IX, XII distributions.
static double	nextCauchy(MersenneTwisterFast randomGenerator) Returns a cauchy distributed random number from the standard Cauchy distribution C(0,1).
static double	nextErlang(double variance, double mean, MersenneTwisterFast randomGenerator) Returns an erlang distributed random number with the given variance and mean.
static int	nextGeometric(double p, MersenneTwisterFast randomGenerator) Returns a discrete geometric distributed random number; Definition.
static double	nextLambda(double l3, double l4, MersenneTwisterFast randomGenerator) Returns a lambda distributed random number with parameters l3 and l4.
static double	nextLaplace(MersenneTwisterFast randomGenerator) Returns a Laplace (Double Exponential) distributed random number from the standard Laplace distribution L(0,1).
static double	nextLogistic(MersenneTwisterFast randomGenerator) Returns a random number from the standard Logistic distribution Log(0,1).
static double	nextPowLaw(double alpha, double cut, MersenneTwisterFast randomGenerator) Returns a power-law distributed random number with the given exponent and lower cutoff.
static double	nextTriangular(MersenneTwisterFast randomGenerator) Returns a random number from the standard Triangular distribution in (-1,1).
static double	nextWeibull(double alpha, double beta, MersenneTwisterFast randomGenerator) Returns a weibull distributed random number.
static int	nextZipfInt(double z, MersenneTwisterFast randomGenerator) Returns a zipfian distributed random number with the given skew.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Distributions

protected Distributions()

Makes this class non instantiable, but still let's others inherit from it.

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,
                               MersenneTwisterFast 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,
                               MersenneTwisterFast 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).

nextCauchy

public static double nextCauchy(MersenneTwisterFast randomGenerator)

Returns a cauchy distributed random number from the standard Cauchy distribution C(0,1). math definition and animated definition.

p(x) = 1/ (mean*pi * (1+(x/mean)^2)).

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

nextErlang

public static double nextErlang(double variance,
                                double mean,
                                MersenneTwisterFast randomGenerator)

Returns an erlang distributed random number with the given variance and mean.

nextGeometric

public static int nextGeometric(double p,
                                MersenneTwisterFast 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,
                                MersenneTwisterFast 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(MersenneTwisterFast 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(MersenneTwisterFast 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,
                                MersenneTwisterFast 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(MersenneTwisterFast 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,
                                 MersenneTwisterFast randomGenerator)

Returns a weibull distributed random number. Polar method. See Simulation, Modelling & Analysis by Law & Kelton, pp259

nextZipfInt

public static int nextZipfInt(double z,
                              MersenneTwisterFast 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).