Distributions

java.lang.Object
- cern.jet.random.Distributions

public class Distributions
extends 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

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`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
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- 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).

Class Distributions

Method Summary

Methods inherited from class java.lang.Object

Method Detail

geometricPdf

nextBurr1

nextBurr2

nextCauchy

nextErlang

nextGeometric

nextLambda

nextLaplace

nextLogistic

nextPowLaw

nextTriangular

nextWeibull

nextZipfInt