neurord.numeric.math

Class Binomial

java.lang.Object

neurord.numeric.math.Binomial

All Implemented Interfaces:

BinomialLike

public class Binomial
extends Object
implements BinomialLike

Binomial distribution; See the math definition and animated definition.

p(x) = k * p^k * (1-p)^(n-k) with k = n! / (k! * (n-k)!).

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Implementation: High performance implementation. Acceptance Rejection/Inversion method. This is a port of RandBinomial used in CLHEP 1.4.0 (C++). CLHEP's implementation is, in turn, based on

V. Kachitvichyanukul, B.W. Schmeiser (1988): Binomial random variate generation, Communications of the ACM 31, 216-222.

Version:

1.0, 09/24/99

Author:

wolfgang.hoschek@cern.ch

Field Summary

Fields

Modifier and Type	Field and Description
protected RandomGenerator	randomGenerator

Constructor Summary

Constructors

Constructor and Description
Binomial(RandomGenerator randomGenerator) Constructs a binomial distribution.

Method Summary

Modifier and Type	Method and Description
protected int	generateBinomial(int n, double p) * Binomial-Distribution - Acceptance Rejection/Inversion * * * Acceptance Rejection method combined with Inversion for * generating Binomial random numbers with parameters * n (number of trials) and p (probability of success).
int	nextInt(int n, double p) Returns a random number from the distribution with the given parameters n and p; bypasses the internal state.

Methods inherited from class java.lang.Object

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

Field Detail

randomGenerator

protected final RandomGenerator randomGenerator

Constructor Detail

Binomial

public Binomial(RandomGenerator randomGenerator)

Constructs a binomial distribution.

Parameters:

randomGenerator - a uniform random number generator.

Method Detail

generateBinomial

protected int generateBinomial(int n,
                               double p)

* Binomial-Distribution - Acceptance Rejection/Inversion * * * Acceptance Rejection method combined with Inversion for * generating Binomial random numbers with parameters * n (number of trials) and p (probability of success). * For min(n*p,n*(1-p)) < 10 the Inversion method is applied: * The random numbers are generated via sequential search, * starting at the lowest index k=0. The cumulative probabilities * are avoided by using the technique of chop-down. * For min(n*p,n*(1-p)) >= 10 Acceptance Rejection is used: * The algorithm is based on a hat-function which is uniform in * the centre region and exponential in the tails. * A triangular immediate acceptance region in the centre speeds * up the generation of binomial variates. * If candidate k is near the mode, f(k) is computed recursively * starting at the mode m. * The acceptance test by Stirling's formula is modified * according to W. Hoermann (1992): The generation of binomial * random variates, to appear in J. Statist. Comput. Simul. * If p < .5 the algorithm is applied to parameters n, p. * Otherwise p is replaced by 1-p, and k is replaced by n - k. * * * FUNCTION: - samples a random number from the binomial * distribution with parameters n and p and is * valid for n*min(p,1-p) > 0. * REFERENCE: - V. Kachitvichyanukul, B.W. Schmeiser (1988): * Binomial random variate generation, * Communications of the ACM 31, 216-222. * SUBPROGRAMS: - StirlingCorrection() * ... Correction term of the Stirling * approximation for log(k!) * (series in 1/k or table values * for small k) with long int k * - randomGenerator ... (0,1)-Uniform engine * *

nextInt

public int nextInt(int n,
                   double p)

Returns a random number from the distribution with the given parameters n and p; bypasses the internal state.

Specified by:

nextInt in interface BinomialLike

Parameters:

n - the number of trials

p - the probability of success.