smile.stat.distribution

Class HyperGeometricDistribution

java.lang.Object

smile.stat.distribution.AbstractDistribution

smile.stat.distribution.DiscreteDistribution

smile.stat.distribution.HyperGeometricDistribution

All Implemented Interfaces:

Distribution

public class HyperGeometricDistribution
extends DiscreteDistribution

The hypergeometric distribution is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement, just as the binomial distribution describes the number of successes for draws with replacement.

Suppose you are to draw "n" balls without replacement from an urn containing "N" balls in total, "m" of which are white. The hypergeometric distribution describes the distribution of the number of white balls drawn from the urn. A random variable X follows the hypergeometric distribution with parameters N, m and n if the probability is given by

              mCk (N-m)C(n-k)
 P(X = k) = ----------------
                   NCn
 

where _nC_k is n choose k.

Constructor Summary

Constructors

Constructor and Description
HyperGeometricDistribution(int N, int m, int n) Constructor.

Method Summary

Modifier and Type	Method and Description
double	cdf(double k) Cumulative distribution function.
double	entropy() Shannon entropy of the distribution.
double	logp(int k) The probability mass function in log scale.
double	mean() The mean of distribution.
int	npara() The number of parameters of the distribution.
double	p(int k) The probability mass function.
double	quantile(double p) The quantile, the probability to the left of quantile is p.
double	rand() Uses inversion by chop-down search from the mode when the mean < 20 and the patchwork-rejection method when the mean > 20.
double	sd() The standard deviation of distribution.
java.lang.String	toString()
double	var() The variance of distribution.

Methods inherited from class smile.stat.distribution.DiscreteDistribution

likelihood, logLikelihood, logp, p, quantile

Methods inherited from class smile.stat.distribution.AbstractDistribution

inverseTransformSampling, likelihood, logLikelihood, quantile, quantile, rejection

Methods inherited from class java.lang.Object

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

Constructor Detail

HyperGeometricDistribution

public HyperGeometricDistribution(int N,
                                  int m,
                                  int n)

Constructor.

Parameters:

N - the number of total samples.

m - the number of defects.

n - the number of draws.

Method Detail

npara

public int npara()

Description copied from interface: Distribution

The number of parameters of the distribution.

mean

public double mean()

Description copied from interface: Distribution

The mean of distribution.

var

public double var()

Description copied from interface: Distribution

The variance of distribution.

sd

public double sd()

Description copied from interface: Distribution

The standard deviation of distribution.

entropy

public double entropy()

Description copied from interface: Distribution

Shannon entropy of the distribution.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

p

public double p(int k)

Description copied from class: DiscreteDistribution

The probability mass function.

Specified by:

p in class DiscreteDistribution

logp

public double logp(int k)

Description copied from class: DiscreteDistribution

The probability mass function in log scale.

Specified by:

logp in class DiscreteDistribution

cdf

public double cdf(double k)

Description copied from interface: Distribution

Cumulative distribution function. That is the probability to the left of x.

quantile

public double quantile(double p)

Description copied from interface: Distribution

The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.

rand

public double rand()

Uses inversion by chop-down search from the mode when the mean < 20 and the patchwork-rejection method when the mean > 20.