Class HypergeometricDistribution

java.lang.Object
org.apache.commons.statistics.distribution.AbstractDiscreteDistribution
org.apache.commons.statistics.distribution.HypergeometricDistribution
All Implemented Interfaces:
DiscreteDistribution
public final class HypergeometricDistribution extends AbstractDiscreteDistribution
Implementation of the hypergeometric distribution.

The probability mass function of \( X \) is:

\[ f(k; N, K, n) = \frac{\binom{K}{k} \binom{N - K}{n-k}}{\binom{N}{n}} \]

for \( N \in \{0, 1, 2, \dots\} \) the population size, \( K \in \{0, 1, \dots, N\} \) the number of success states, \( n \in \{0, 1, \dots, N\} \) the number of samples, \( k \in \{\max(0, n+K-N), \dots, \min(n, K)\} \) the number of successes, and

\[ \binom{a}{b} = \frac{a!}{b! \, (a-b)!} \]

is the binomial coefficient.

See Also:

  • Nested Class Summary

    Nested classes/interfaces inherited from interface DiscreteDistribution

    DiscreteDistribution.Sampler

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private final double
    bp
    Binomial probability of success (sampleSize / populationSize).
    private final double
    bq
    Binomial probability of failure ((populationSize - sampleSize) / populationSize).
    private static final double
    HALF
    1/2.
    private final int
    lowerBound
    The lower bound of the support (inclusive).
    private double[]
    midpoint
    Cached midpoint of the CDF/SF.
    private final int
    numberOfSuccesses
    The number of successes in the population.
    private final int
    populationSize
    The population size.
    private final int
    sampleSize
    The sample size.
    private final int
    upperBound
    The upper bound of the support (inclusive).

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    private
    HypergeometricDistribution(int populationSize, int numberOfSuccesses, int sampleSize)
     

  • Method Summary

    Modifier and Type
    Method
    Description
    private int
    computeInverseProbability(double p, double q, boolean complement)
    Implementation for the inverse cumulative or survival probability.
    private double
    computeLogProbability(int x)
    Compute the log probability.
    double
    cumulativeProbability(int x)
    For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
    private static int
    getLowerDomain(int nn, int k, int n)
    Return the lowest domain value for the given hypergeometric distribution parameters.
    double
    getMean()
    Gets the mean of this distribution.
    private double[]
    getMidPoint()
    Return the mid-point x of the distribution, and the cdf(x).
    int
    getNumberOfSuccesses()
    Gets the number of successes parameter of this distribution.
    int
    getPopulationSize()
    Gets the population size parameter of this distribution.
    int
    getSampleSize()
    Gets the sample size parameter of this distribution.
    int
    getSupportLowerBound()
    Gets the lower bound of the support.
    int
    getSupportUpperBound()
    Gets the upper bound of the support.
    private static int
    getUpperDomain(int k, int n)
    Return the highest domain value for the given hypergeometric distribution parameters.
    double
    getVariance()
    Gets the variance of this distribution.
    private double
    innerCumulativeProbability(int x0, int x1)
    For this distribution, X, this method returns P(x0 <= X <= x1).
    int
    inverseCumulativeProbability(double p)
    Computes the quantile function of this distribution.
    private int
    inverseLower(double p, double q, boolean complement)
    Compute the inverse cumulative or survival probability using the lower sum.
    int
    inverseSurvivalProbability(double p)
    Computes the inverse survival probability function of this distribution.
    private int
    inverseUpper(double p, double q, boolean complement)
    Compute the inverse cumulative or survival probability using the upper sum.
    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.
    static HypergeometricDistribution
    of(int populationSize, int numberOfSuccesses, int sampleSize)
    Creates a hypergeometric distribution.
    double
    probability(int x)
    For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
    double
    probability(int x0, int x1)
    For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
    double
    survivalProbability(int x)
    For a random variable X whose values are distributed according to this distribution, this method returns P(X > x).

    Methods inherited from class AbstractDiscreteDistribution

    createSampler, getMedian

    Methods inherited from class Object

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

  • Field Details

    • HALF

      private static final double HALF
      1/2.
      See Also:

    • 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.

    • lowerBound

      private final int lowerBound
      The lower bound of the support (inclusive).

    • upperBound

      private final int upperBound
      The upper bound of the support (inclusive).

    • bp

      private final double bp
      Binomial probability of success (sampleSize / populationSize).

    • bq

      private final double bq
      Binomial probability of failure ((populationSize - sampleSize) / populationSize).

    • midpoint

      private double[] midpoint
      Cached midpoint of the CDF/SF. The array holds [x, cdf(x)] for the midpoint x. Used for the cumulative probability functions.

  • Constructor Details

    • HypergeometricDistribution

      private HypergeometricDistribution(int populationSize, int numberOfSuccesses, int sampleSize)
      Parameters:
      populationSize - Population size.
      numberOfSuccesses - Number of successes in the population.
      sampleSize - Sample size.

  • Method Details

    • of

      public static HypergeometricDistribution of(int populationSize, int numberOfSuccesses, int sampleSize)
      Creates a hypergeometric distribution.
      Parameters:
      populationSize - Population size.
      numberOfSuccesses - Number of successes in the population.
      sampleSize - Sample size.
      Returns:
      the distribution
      Throws:
      IllegalArgumentException - if numberOfSuccesses < 0, or populationSize <= 0 or numberOfSuccesses > populationSize, or sampleSize > populationSize.

    • getLowerDomain

      private static int getLowerDomain(int nn, int k, int n)
      Return the lowest domain value for the given hypergeometric distribution parameters.
      Parameters:
      nn - Population size.
      k - Number of successes in the population.
      n - Sample size.
      Returns:
      the lowest domain value of the hypergeometric distribution.

    • getUpperDomain

      private static int getUpperDomain(int k, int n)
      Return the highest domain value for the given hypergeometric distribution parameters.
      Parameters:
      k - Number of successes in the population.
      n - Sample size.
      Returns:
      the highest domain value of the hypergeometric distribution.

    • getPopulationSize

      public int getPopulationSize()
      Gets the population size parameter of this distribution.
      Returns:
      the population size.

    • getNumberOfSuccesses

      public int getNumberOfSuccesses()
      Gets the number of successes parameter of this distribution.
      Returns:
      the number of successes.

    • getSampleSize

      public int getSampleSize()
      Gets the sample size parameter of this distribution.
      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 - Point at which the PMF is evaluated.
      Returns:
      the value of the probability mass function at x.

    • probability

      public double probability(int x0, int x1)
      For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1). The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

      Special cases:

      • returns 0.0 if x0 == x1;
      • returns probability(x1) if x0 + 1 == x1;
      Specified by:
      probability in interface DiscreteDistribution
      Overrides:
      probability in class AbstractDiscreteDistribution
      Parameters:
      x0 - Lower bound (exclusive).
      x1 - Upper bound (inclusive).
      Returns:
      the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.

    • 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.
      Parameters:
      x - Point at which the PMF is evaluated.
      Returns:
      the logarithm of the value of the probability mass function at x.

    • computeLogProbability

      private double computeLogProbability(int x)
      Compute the log probability.
      Parameters:
      x - Value.
      Returns:
      log(P(X = x))

    • 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 - 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.

    • survivalProbability

      public double survivalProbability(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 complementary cumulative distribution function.

      By default, this is defined as 1 - cumulativeProbability(x), but the specific implementation may be more accurate.

      Parameters:
      x - Point at which the survival function is evaluated.
      Returns:
      the probability that a random variable with this distribution takes a value greater than x.

    • innerCumulativeProbability

      private double innerCumulativeProbability(int x0, int x1)
      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 + dx, x0 + 2 * dx, ..., x1; the direction dx is determined using a comparison of the input bounds. This should be called by using x0 as the domain limit and x1 as the internal value. This will result in an initial sum of increasing larger magnitudes.
      Parameters:
      x0 - Inclusive domain bound.
      x1 - Inclusive internal bound.
      Returns:
      P(x0 <= X <= x1).

    • inverseCumulativeProbability

      public int inverseCumulativeProbability(double p)
      Description copied from class: AbstractDiscreteDistribution
      Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is:

      \[ x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \le x) \ge p\} & \text{for } 0 \lt p \le 1 \\ \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} & \text{for } p = 0 \end{cases} \]

      If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned. In this case the result of cumulativeProbability(x) called using the returned p-quantile may not compute the original p.

      The default implementation returns:

      Specified by:
      inverseCumulativeProbability in interface DiscreteDistribution
      Overrides:
      inverseCumulativeProbability in class AbstractDiscreteDistribution
      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0).

    • inverseSurvivalProbability

      public int inverseSurvivalProbability(double p)
      Description copied from class: AbstractDiscreteDistribution
      Computes the inverse survival probability function of this distribution. For a random variable X distributed according to this distribution, the returned value is:

      \[ x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \gt x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb Z : P(X \gt x) \lt 1 \} & \text{for } p = 1 \end{cases} \]

      If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned. In this case the result of survivalProbability(x) called using the returned (1-p)-quantile may not compute the original p.

      By default, this is defined as inverseCumulativeProbability(1 - p), but the specific implementation may be more accurate.

      The default implementation returns:

      Specified by:
      inverseSurvivalProbability in interface DiscreteDistribution
      Overrides:
      inverseSurvivalProbability in class AbstractDiscreteDistribution
      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest (1-p)-quantile of this distribution (largest 0-quantile for p = 1).

    • computeInverseProbability

      private int computeInverseProbability(double p, double q, boolean complement)
      Implementation for the inverse cumulative or survival probability.
      Parameters:
      p - Cumulative probability.
      q - Survival probability.
      complement - Set to true to compute the inverse survival probability.
      Returns:
      the value

    • inverseLower

      private int inverseLower(double p, double q, boolean complement)
      Compute the inverse cumulative or survival probability using the lower sum.
      Parameters:
      p - Cumulative probability.
      q - Survival probability.
      complement - Set to true to compute the inverse survival probability.
      Returns:
      the value

    • inverseUpper

      private int inverseUpper(double p, double q, boolean complement)
      Compute the inverse cumulative or survival probability using the upper sum.
      Parameters:
      p - Cumulative probability.
      q - Survival probability.
      complement - Set to true to compute the inverse survival probability.
      Returns:
      the value

    • getMean

      public double getMean()
      Gets the mean of this distribution.

      For population size \( N \), number of successes \( K \), and sample size \( n \), the mean is:

      \[ n \frac{K}{N} \]

      Returns:
      the mean.

    • getVariance

      public double getVariance()
      Gets the variance of this distribution.

      For population size \( N \), number of successes \( K \), and sample size \( n \), the variance is:

      \[ n \frac{K}{N} \frac{N-K}{N} \frac{N-n}{N-1} \]

      Returns:
      the variance.

    • getSupportLowerBound

      public int getSupportLowerBound()
      Gets the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0), i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} \). By convention, Integer.MIN_VALUE should be substituted for negative infinity.

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

      Returns:
      lower bound of the support

    • getSupportUpperBound

      public int getSupportUpperBound()
      Gets the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1), i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) = 1 \} \). By convention, Integer.MAX_VALUE should be substituted for positive infinity.

      For number of successes \( K \), and sample size \( n \), the upper bound of the support is \( \min \{ n, K \} \).

      Returns:
      upper bound of the support

    • getMidPoint

      private double[] getMidPoint()
      Return the mid-point x of the distribution, and the cdf(x).

      This is not the true median. It is the value where the CDF(x) is closest to 0.5; as such the CDF may be below 0.5 if the next value of x is further from 0.5.

      Returns:
      the mid-point ([x, cdf(x)])