Class Binomial

All Implemented Interfaces:
Serializable

public class Binomial extends AbstractDiscreteDistribution
Binomial distribution; See the math definition and animated definition.

p(k) = C(n,k) * p^k * (1-p)^(n-k) with C(n,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:
  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    protected int
     
    protected double
     

    Fields inherited from class sim.util.distribution.AbstractDistribution

    randomGenerator
  • Constructor Summary

    Constructors
    Constructor
    Description
    Binomial(int n, double p, MersenneTwisterFast randomGenerator)
    Constructs a binomial distribution.
  • Method Summary

    Modifier and Type
    Method
    Description
    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
    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.
    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 Details

    • n

      protected int n
    • p

      protected double p
  • Constructor Details

    • 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:
      IllegalArgumentException - if n*Math.min(p,1-p) <= 0.0
  • Method Details

    • 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)) invalid input: '<' 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 invalid input: '<' .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:
      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:
      IllegalArgumentException - if n*Math.min(p,1-p) <= 0.0
    • toString

      public String toString()
      Returns a String representation of the receiver.
      Overrides:
      toString in class Object