org.apache.commons.math3.distribution

## 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 org.apache.commons.math3.distribution.AbstractIntegerDistribution

      `random, randomData`

  - ### Constructor Summary

    Constructors
    Constructor and 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

    Methods
    Modifier and Type | Method and 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.
    `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 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`

- - ### 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.

      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 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`

    - #### 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 <= 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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