Class HypergeometricDistribution

java.lang.Object

org.apache.commons.math3.distribution.AbstractIntegerDistribution

org.apache.commons.math3.distribution.HypergeometricDistribution

All Implemented Interfaces:

Serializable, IntegerDistribution

public class HypergeometricDistribution
extends AbstractIntegerDistribution

Implementation of the hypergeometric distribution.

See Also:

• Hypergeometric distribution (Wikipedia)
• Hypergeometric distribution (MathWorld)
• Serialized Form

Field Summary

Fields inherited from class AbstractIntegerDistribution

random, randomData

Constructor Summary

Constructors

Constructor	Description
HypergeometricDistribution(int populationSize, int numberOfSuccesses, int sampleSize)	Construct a new hypergeometric distribution with the specified population size, number of successes in the population, and sample size.
HypergeometricDistribution(RandomGenerator rng, int populationSize, int numberOfSuccesses, int sampleSize)	Creates a new hypergeometric distribution.

Method Summary

Modifier and Type	Method	Description
protected double	calculateNumericalVariance()	Used by getNumericalVariance().
double	cumulativeProbability(int x)	For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
int	getNumberOfSuccesses()	Access the number of successes.
double	getNumericalMean()	Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance()	Use this method to get the numerical value of the variance of this distribution.
int	getPopulationSize()	Access the population size.
int	getSampleSize()	Access the sample size.
int	getSupportLowerBound()	Access the lower bound of the support.
int	getSupportUpperBound()	Access the upper bound of the support.
boolean	isSupportConnected()	Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support.
double	logProbability(int x)	For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.
double	probability(int x)	For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
double	upperCumulativeProbability(int x)	For this distribution, X, this method returns P(X >= x).

Methods inherited from class AbstractIntegerDistribution

cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample, sample, solveInverseCumulativeProbability

Methods inherited from class Object

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

Constructor Details

HypergeometricDistribution

public HypergeometricDistribution(int populationSize,
 int numberOfSuccesses,
 int sampleSize)
                           throws NotPositiveException,
NotStrictlyPositiveException,
NumberIsTooLargeException

Construct a new hypergeometric distribution with the specified population size, number of successes in the population, and sample size.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractIntegerDistribution.sample() and AbstractIntegerDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

Parameters:

populationSize - Population size.

numberOfSuccesses - Number of successes in the population.

sampleSize - Sample size.

Throws:

NotPositiveException - if numberOfSuccesses < 0.

NotStrictlyPositiveException - if populationSize <= 0.

NumberIsTooLargeException - if numberOfSuccesses > populationSize, or sampleSize > populationSize.

HypergeometricDistribution

public HypergeometricDistribution(RandomGenerator rng,
 int populationSize,
 int numberOfSuccesses,
 int sampleSize)
                           throws NotPositiveException,
NotStrictlyPositiveException,
NumberIsTooLargeException

Creates a new hypergeometric distribution.

Parameters:

rng - Random number generator.

populationSize - Population size.

numberOfSuccesses - Number of successes in the population.

sampleSize - Sample size.

Throws:

NotPositiveException - if numberOfSuccesses < 0.

NotStrictlyPositiveException - if populationSize <= 0.

NumberIsTooLargeException - if numberOfSuccesses > populationSize, or sampleSize > populationSize.

Since:

3.1

Method Details

cumulativeProbability

public double cumulativeProbability(int x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.

Parameters:

x - the point at which the CDF is evaluated

Returns:

the probability that a random variable with this distribution takes a value less than or equal to x

getNumberOfSuccesses

public int getNumberOfSuccesses()

Access the number of successes.

Returns:

the number of successes.

getPopulationSize

public int getPopulationSize()

Access the population size.

Returns:

the population size.

getSampleSize

public int getSampleSize()

Access the sample size.

Returns:

the sample size.

probability

public double probability(int x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X = x). In other words, this method represents the probability mass function (PMF) for the distribution.

Parameters:

x - the point at which the PMF is evaluated

Returns:

the value of the probability mass function at x

logProbability

public double logProbability(int x)

For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm. In other words, this method represents the logarithm of the probability mass function (PMF) for the distribution. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of IntegerDistribution.probability(int).

The default implementation simply computes the logarithm of probability(x).

Overrides:

logProbability in class AbstractIntegerDistribution

Parameters:

x - the point at which the PMF is evaluated

Returns:

the logarithm of the value of the probability mass function at x

upperCumulativeProbability

public double upperCumulativeProbability(int x)

For this distribution, X, this method returns P(X >= x).

Parameters:

x - Value at which the CDF is evaluated.

Returns:

the upper tail CDF for this distribution.

Since:

1.1

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution. For population size N, number of successes m, and sample size n, the mean is n * m / N.

Returns:

the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution. For population size N, number of successes m, and sample size n, the variance is [n * m * (N - n) * (N - m)] / [N^2 * (N - 1)].

Returns:

the variance (possibly Double.POSITIVE_INFINITY or Double.NaN if it is not defined)

calculateNumericalVariance

protected double calculateNumericalVariance()

Used by getNumericalVariance().

Returns:

the variance of this distribution

getSupportLowerBound

public int getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in Z | P(X invalid input: '<'= x) > 0}.

For population size N, number of successes m, and sample size n, the lower bound of the support is max(0, n + m - N).

Returns:

lower bound of the support

getSupportUpperBound

public int getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X invalid input: '<'= x) = 1}.

For number of successes m and sample size n, the upper bound of the support is min(m, n).

Returns:

upper bound of the support

isSupportConnected

public boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Returns:

true