cern.jet.random
Class Distributions

java.lang.Object
  extended by cern.jet.random.Distributions

public class Distributions
extends java.lang.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);
    ...
 }
 

Author:
wolfgang.hoschek@cern.ch
See Also:
MersenneTwister, Random, Math

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, RandomEngine randomGenerator)
          Returns a random number from the Burr II, VII, VIII, X Distributions.
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.
static double nextCauchy(RandomEngine randomGenerator)
          Returns a cauchy distributed random number from the standard Cauchy distribution C(0,1).
static double nextErlang(double variance, double mean, RandomEngine randomGenerator)
          Returns an erlang distributed random number with the given variance and mean.
static int nextGeometric(double p, RandomEngine randomGenerator)
          Returns a discrete geometric distributed random number; Definition.
static double nextLambda(double l3, double l4, RandomEngine randomGenerator)
          Returns a lambda distributed random number with parameters l3 and l4.
static double nextLaplace(RandomEngine randomGenerator)
          Returns a Laplace (Double Exponential) distributed random number from the standard Laplace distribution L(0,1).
static double nextLogistic(RandomEngine randomGenerator)
          Returns a random number from the standard Logistic distribution Log(0,1).
static double nextPowLaw(double alpha, double cut, RandomEngine randomGenerator)
          Returns a power-law distributed random number with the given exponent and lower cutoff.
static double nextTriangular(RandomEngine randomGenerator)
          Returns a random number from the standard Triangular distribution in (-1,1).
static double nextWeibull(double alpha, double beta, RandomEngine randomGenerator)
          Returns a weibull distributed random number.
static int nextZipfInt(double z, RandomEngine 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,
                               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).

nextCauchy

public static double nextCauchy(RandomEngine 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,
                                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).