Interface DiscreteDistribution

All Known Implementing Classes:
AbstractDiscreteDistribution, BinomialDistribution, GeometricDistribution, HypergeometricDistribution, PascalDistribution, PoissonDistribution, UniformDiscreteDistribution, ZipfDistribution

public interface DiscreteDistribution
Interface for distributions on the integers.
  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Interface
    Description
    static interface 
    Distribution sampling functionality.
  • Method Summary

    Modifier and Type
    Method
    Description
    createSampler(org.apache.commons.rng.UniformRandomProvider rng)
    Creates a sampler.
    double
    For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
    double
    Gets the mean of this distribution.
    int
    Gets the lower bound of the support.
    int
    Gets the upper bound of the support.
    double
    Gets the variance of this distribution.
    int
    Computes the quantile function of this distribution.
    default int
    Computes the inverse survival probability function of this distribution.
    default double
    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).
    default 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).
    default double
    For a random variable X whose values are distributed according to this distribution, this method returns P(X > x).
  • Method Details

    • probability

      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

      default 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;
      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.
      Throws:
      IllegalArgumentException - if x0 > x1.
    • logProbability

      default 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.
    • cumulativeProbability

      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

      default 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.
    • inverseCumulativeProbability

      int inverseCumulativeProbability(double p)
      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.

      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0).
      Throws:
      IllegalArgumentException - if p < 0 or p > 1.
    • inverseSurvivalProbability

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

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

      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.

      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest (1-p)-quantile of this distribution (largest 0-quantile for p = 1).
      Throws:
      IllegalArgumentException - if p < 0 or p > 1.
    • getMean

      double getMean()
      Gets the mean of this distribution.
      Returns:
      the mean.
    • getVariance

      double getVariance()
      Gets the variance of this distribution.
      Returns:
      the variance.
    • getSupportLowerBound

      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.
      Returns:
      the lower bound of the support.
    • getSupportUpperBound

      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.
      Returns:
      the upper bound of the support.
    • createSampler

      DiscreteDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
      Creates a sampler.
      Parameters:
      rng - Generator of uniformly distributed numbers.
      Returns:
      a sampler that produces random numbers according this distribution.