eduni.distributions
Class Distributions

java.lang.Object
  |
  +--eduni.distributions.Distributions

public class Distributions

extends java.lang.Object

offers several discrete and continuous distributions all seeded by a common well-spaced pseudo random number generator (PRNG).

Constructor Summary

Distributions()
The seed is automatically provided by a well-spaced SeedGenerator

Distributions(ContinuousGenerator gen)
This constructor allows for manually specially the continous generator shared to compute the distribution function.

Distributions(long seed)
The seed is manually set

Method Summary

long	bernoulli(double prob) computes a Bernoulli's distribution
double	beta(double shape_a, double shape_b) computes a beta distribution using Cheng's method (1978) when shape_a>1 or shape_b>1 and Berman's method (1970) otherwise
double	betaprime(double shape_a, double shape_b) computes a beta prime distribution
long	binomial(double prob, int trials) computes a binomial distribution
double	cauchy(double median, double scale) computes a Cauchy's distribution
double	chisquare(long deg_freedom) computes a chisquare distribution
double	erlang(double scale, double shape) computes an Erlang's distribution
double	f(long num_deg_freedom, long den_deg_freedom) computes a F distribution
double	gamma(double scale, double shape) computes a gamma distribution
long	geometric(double prob) computes a geometric distribution
double	invgamma(double scale, double shape) computes an invgamma distribution
double	logistic(double location, double scale) computes a logistic distribution
double	lognormal(double mean, double variance) computes a lognormal distribution
double	lognormal2(double mean, double std_dev) computes a lognormal distribution
double	negexp(double mean) computes a negexp distribution
double	normal(double mean, double variance) computes a normal distribution; sample are provided by the same PRGN
double	normal2(double mean, double std_dev) computes a normal distribution; sample are provided by the same PRGN
double	pareto(double scale, double shape) computes a pareto distribution; sample is provided by the PRGN
long	pascal(double prob, int successes) computes a Pascal's distribution
long	poisson(double mean) computes a poisson distribution
double	tstudent(long deg_freedom) computes a tstudent distribution; sample is provided by the PRGN
double	uniform(double min, double max) computes a uniform distribution; sample is provided by the PRGN
double	weibull(double scale, double shape) computes a weibull distribution; sample is provided by the PRGN

Methods inherited from class java.lang.Object

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

Constructor Detail

Distributions

public Distributions()

The seed is automatically provided by a well-spaced SeedGenerator

Distributions

public Distributions(long seed)

The seed is manually set

Distributions

public Distributions(ContinuousGenerator gen)

This constructor allows for manually specially the continous generator shared to compute the distribution function.

Method Detail

bernoulli

public long bernoulli(double prob)

computes a Bernoulli's distribution

Returns:

1 iif sample ≤ prob, 0 otherwise; sample is provided by the PRGN

binomial

public long binomial(double prob,
                     int trials)

computes a binomial distribution

Returns:

∑(i=0; i<trials-1; bernoulli(prob))

geometric

public long geometric(double prob)

computes a geometric distribution

Returns:

⌈ log(sample)/log(1-prob) ⌉; sample is provided by the PRGN

pascal

public long pascal(double prob,
                   int successes)

computes a Pascal's distribution

Returns:

∑(i=0; i<successes; geometric(prob))

poisson

public long poisson(double mean)

computes a poisson distribution

Returns:

the smallest integer x so as ∏(i=0; i<x; sample) ≤ exp(-mean)

beta

public double beta(double shape_a,
                   double shape_b)

computes a beta distribution using Cheng's method (1978) when shape_a>1 or shape_b>1 and Berman's method (1970) otherwise

betaprime

public double betaprime(double shape_a,
                        double shape_b)

computes a beta prime distribution

Returns:

1/beta(shape_a, shape_b) - 1

cauchy

public double cauchy(double median,
                     double scale)

computes a Cauchy's distribution

Returns:

median + scale/tan(Π * sample); sample is provided by the PRGN

chisquare

public double chisquare(long deg_freedom)

computes a chisquare distribution

Returns:

∑(i=0; i<deg_freedom; normal(0,1))

erlang

public double erlang(double scale,
                     double shape)

computes an Erlang's distribution

Returns:

-scale * log ( ∏(i=0; i<shape; sample) ); sample is provided by the PRGN

f

public double f(long num_deg_freedom,
                long den_deg_freedom)

computes a F distribution

Returns:

chisquare(num_deg_freedom)/num_deg_freedom / chisquare(den_deg_freedom)/den_deg_freedom

gamma

public double gamma(double scale,
                    double shape)

computes a gamma distribution

invgamma

public double invgamma(double scale,
                       double shape)

computes an invgamma distribution

Returns:

1.0/gamma(scale, shape)

logistic

public double logistic(double location,
                       double scale)

computes a logistic distribution

Returns:

location - scale * log (1/sample - 1)

lognormal

public double lognormal(double mean,
                        double variance)

computes a lognormal distribution

Returns:

exp(mean + √variance * normal(0,1))

lognormal2

public double lognormal2(double mean,
                         double std_dev)

computes a lognormal distribution

Parameters:

std_dev - is assumed to be the square root of the variance.

Returns:

exp(mean + std_dev * normal(0,1))

negexp

public double negexp(double mean)

computes a negexp distribution

Returns:

-mean * log (sample); where sample is provided by the PRGN

normal

public double normal(double mean,
                     double variance)

computes a normal distribution; sample are provided by the same PRGN

Returns:

mean + √(variance) * cos (2Π * sample) * √(-2 * log (sample))

normal2

public double normal2(double mean,
                      double std_dev)

computes a normal distribution; sample are provided by the same PRGN

Parameters:

std_dev - is assumed to be the square root of the variance.

Returns:

mean + std_dev * cos (2Π * sample) * √(-2 * log (sample))

pareto

public double pareto(double scale,
                     double shape)

computes a pareto distribution; sample is provided by the PRGN

Returns:

scale / (sample^(1/shape))

tstudent

public double tstudent(long deg_freedom)

computes a tstudent distribution; sample is provided by the PRGN

Returns:

normal(0,1)/√(chisquare(deg_freedom)/deg_freedom)

uniform

public double uniform(double min,
                      double max)

computes a uniform distribution; sample is provided by the PRGN

Returns:

min + (max-min) * sample

weibull

public double weibull(double scale,
                      double shape)

computes a weibull distribution; sample is provided by the PRGN

Returns:

scale * (sample ^ (1/shape))