sim.util.distribution
Class Binomial

java.lang.Object
  sim.util.distribution.AbstractDistribution
      sim.util.distribution.AbstractDiscreteDistribution
          sim.util.distribution.Binomial

All Implemented Interfaces:

java.io.Serializable

public class Binomial
extends AbstractDiscreteDistribution

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.

See Also:

Serialized Form

Field Summary

protected int	n
protected double	p

Fields inherited from class sim.util.distribution.AbstractDistribution

randomGenerator

Constructor Summary

Binomial(int n, double p, MersenneTwisterFast randomGenerator)
Constructs a binomial distribution.

Method Summary

double	cdf(int k) Returns the cumulative distribution function.
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() Returns a random number from the distribution.
int	nextInt(int n, double p) Returns a random number from the distribution with the given parameters n and p; bypasses the internal state.
double	pdf(int k) Returns the probability distribution function.
void	setNandP(int n, double p) Sets the parameters number of trials and the probability of success.
java.lang.String	toString() Returns a String representation of the receiver.

Methods inherited from class sim.util.distribution.AbstractDiscreteDistribution

nextDouble

Methods inherited from class sim.util.distribution.AbstractDistribution

apply, apply, getRandomGenerator, setRandomGenerator

Methods inherited from class java.lang.Object

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

Field Detail

n

protected int n

p

protected double p

Constructor Detail

Binomial

public Binomial(int n,
                double p,
                MersenneTwisterFast randomGenerator)

Constructs a binomial distribution. Example: n=1, p=0.5.

Parameters:

n - the number of trials (also known as sample size).

p - the probability of success.

randomGenerator - a uniform random number generator.

Throws:

java.lang.IllegalArgumentException - if n*Math.min(p,1-p) <= 0.0

Method Detail

cdf

public double cdf(int k)

Returns the cumulative distribution function.

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()

Returns a random number from the distribution.

Specified by:

nextInt in class AbstractDiscreteDistribution

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.

Parameters:

n - the number of trials

p - the probability of success.

Throws:

java.lang.IllegalArgumentException - if n*Math.min(p,1-p) <= 0.0

pdf

public double pdf(int k)

Returns the probability distribution function.

setNandP

public void setNandP(int n,
                     double p)

Sets the parameters number of trials and the probability of success.

Parameters:

n - the number of trials

p - the probability of success.

Throws:

java.lang.IllegalArgumentException - if n*Math.min(p,1-p) <= 0.0

toString

public java.lang.String toString()

Returns a String representation of the receiver.

Overrides:

toString in class java.lang.Object