org.apache.commons.math3.distribution
Class HypergeometricDistribution

java.lang.Object
  extended by org.apache.commons.math3.distribution.AbstractIntegerDistribution
      extended by org.apache.commons.math3.distribution.HypergeometricDistribution
All Implemented Interfaces:
Serializable, IntegerDistribution

public class HypergeometricDistribution
extends AbstractIntegerDistribution

Implementation of the hypergeometric distribution.

Version:
$Id: HypergeometricDistribution.java 1244107 2012-02-14 16:17:55Z erans $
See Also:
Hypergeometric distribution (Wikipedia), Hypergeometric distribution (MathWorld), Serialized Form

Field Summary
private  int numberOfSuccesses
          The number of successes in the population.
private  double numericalVariance
          Cached numerical variance
private  boolean numericalVarianceIsCalculated
          Whether or not the numerical variance has been calculated
private  int populationSize
          The population size.
private  int sampleSize
          The sample size.
private static long serialVersionUID
          Serializable version identifier.
 
Fields inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution
randomData
 
Constructor Summary
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.
 
Method Summary
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).
private  int[] getDomain(int n, int m, int k)
          Return the domain for the given hypergeometric distribution parameters.
private  int getLowerDomain(int n, int m, int k)
          Return the lowest domain value for the given hypergeometric distribution parameters.
 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.
private  int getUpperDomain(int m, int k)
          Return the highest domain value for the given hypergeometric distribution parameters.
private  double innerCumulativeProbability(int x0, int x1, int dx, int n, int m, int k)
          For this distribution, X, this method returns P(x0 <= X <= x1).
 boolean isSupportConnected()
          Use this method to get information about whether the support is connected, i.e.
 double probability(int x)
          For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
private  double probability(int n, int m, int k, int x)
          For this distribution, X, defined by the given hypergeometric distribution parameters, this method returns P(X = x).
 double upperCumulativeProbability(int x)
          For this distribution, X, this method returns P(X >= x).
 
Methods inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution
cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample, sample, solveInverseCumulativeProbability
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

serialVersionUID

private static final long serialVersionUID
Serializable version identifier.

See Also:
Constant Field Values

numberOfSuccesses

private final int numberOfSuccesses
The number of successes in the population.


populationSize

private final int populationSize
The population size.


sampleSize

private final int sampleSize
The sample size.


numericalVariance

private double numericalVariance
Cached numerical variance


numericalVarianceIsCalculated

private boolean numericalVarianceIsCalculated
Whether or not the numerical variance has been calculated

Constructor Detail

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.

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.
Method Detail

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

getDomain

private int[] getDomain(int n,
                        int m,
                        int k)
Return the domain for the given hypergeometric distribution parameters.

Parameters:
n - Population size.
m - Number of successes in the population.
k - Sample size.
Returns:
a two element array containing the lower and upper bounds of the hypergeometric distribution.

getLowerDomain

private int getLowerDomain(int n,
                           int m,
                           int k)
Return the lowest domain value for the given hypergeometric distribution parameters.

Parameters:
n - Population size.
m - Number of successes in the population.
k - Sample size.
Returns:
the lowest domain value of the hypergeometric distribution.

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.

getUpperDomain

private int getUpperDomain(int m,
                           int k)
Return the highest domain value for the given hypergeometric distribution parameters.

Parameters:
m - Number of successes in the population.
k - Sample size.
Returns:
the highest domain value of the hypergeometric distribution.

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

probability

private double probability(int n,
                           int m,
                           int k,
                           int x)
For this distribution, X, defined by the given hypergeometric distribution parameters, this method returns P(X = x).

Parameters:
x - Value at which the PMF is evaluated.
n - the population size.
m - number of successes in the population.
k - the sample size.
Returns:
PMF for the distribution.

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

innerCumulativeProbability

private double innerCumulativeProbability(int x0,
                                          int x1,
                                          int dx,
                                          int n,
                                          int m,
                                          int k)
For this distribution, X, this method returns P(x0 <= X <= x1). This probability is computed by summing the point probabilities for the values x0, x0 + 1, x0 + 2, ..., x1, in the order directed by dx.

Parameters:
x0 - Inclusive lower bound.
x1 - Inclusive upper bound.
dx - Direction of summation (1 indicates summing from x0 to x1, and 0 indicates summing from x1 to x0).
n - the population size.
m - number of successes in the population.
k - the sample size.
Returns:
P(x0 <= X <= x1).

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 <= 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 <= 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


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