Package org.apache.commons.statistics.distribution

Class UniformDiscreteDistribution

java.lang.Object
org.apache.commons.statistics.distribution.UniformDiscreteDistribution
All Implemented Interfaces:
DiscreteDistribution
public class UniformDiscreteDistribution
extends java.lang.Object
Implementation of the uniform integer distribution.

  • Nested Class Summary

    Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.DiscreteDistribution

    DiscreteDistribution.Sampler

  • Constructor Summary

    Constructors 
    Constructor Description
    UniformDiscreteDistribution​(int lower, int upper)
    Creates a new uniform integer distribution using the given lower and upper bounds (both inclusive).

  • Method Summary

    Modifier and Type Method Description
    DiscreteDistribution.Sampler createSampler​(UniformRandomProvider rng)
    Creates a sampler.
    double cumulativeProbability​(int x)
    For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
    double getMean()
    Gets the mean of this distribution.
    int getSupportLowerBound()
    Gets the lower bound of the support.
    int getSupportUpperBound()
    Gets the upper bound of the support.
    double getVariance()
    Gets the variance of this distribution.
    int inverseCumulativeProbability​(double p)
    Computes the quantile function of this distribution.
    boolean isSupportConnected()
    Indicates 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).
    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).
    static int[] sample​(int n, DiscreteDistribution.Sampler sampler)
    Utility function for allocating an array and filling it with n samples generated by the given sampler.

    Methods inherited from class java.lang.Object

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

    Methods inherited from interface org.apache.commons.statistics.distribution.DiscreteDistribution

    logProbability

  • Constructor Details

    • UniformDiscreteDistribution

      public UniformDiscreteDistribution​(int lower, int upper)
      Creates a new uniform integer distribution using the given lower and upper bounds (both inclusive).
      Parameters:
      lower - Lower bound (inclusive) of this distribution.
      upper - Upper bound (inclusive) of this distribution.
      Throws:
      java.lang.IllegalArgumentException - if lower > upper.

  • Method Details

    • 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.

    • 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.

    • getMean

      public double getMean()
      Gets the mean of this distribution. For lower bound lower and upper bound upper, the mean is 0.5 * (lower + upper).
      Returns:
      the mean, or Double.NaN if it is not defined.

    • getVariance

      public double getVariance()
      Gets the variance of this distribution. For lower bound lower and upper bound upper, and n = upper - lower + 1, the variance is (n^2 - 1) / 12.
      Returns:
      the variance, or Double.NaN if it is not defined.

    • 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 Z | P(X <= x) > 0}. By convention, Integer.MIN_VALUE should be substituted for negative infinity. The lower bound of the support is equal to the lower bound parameter of the distribution.
      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 R | P(X <= x) = 1}. By convention, Integer.MAX_VALUE should be substituted for positive infinity. The upper bound of the support is equal to the upper bound parameter of the distribution.
      Returns:
      upper bound of the support

    • isSupportConnected

      public boolean isSupportConnected()
      Indicates 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

    • createSampler

      public DiscreteDistribution.Sampler createSampler​(UniformRandomProvider rng)
      Creates a sampler.
      Specified by:
      createSampler in interface DiscreteDistribution
      Parameters:
      rng - Generator of uniformly distributed numbers.
      Returns:
      a sampler that produces random numbers according this distribution.

    • 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)
      Specified by:
      probability in interface DiscreteDistribution
      Parameters:
      x0 - Lower bound (exclusive).
      x1 - Upper bound (inclusive).
      Returns:
      the probability that a random variable with this distribution will take a value between x0 and x1, excluding the lower and including the upper endpoint.

    • inverseCumulativeProbability

      public 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
      • inf{x in Z | P(X<=x) >= p} for 0 < p <= 1,
      • inf{x in Z | P(X<=x) > 0} for p = 0.
      If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned. The default implementation returns
      Specified by:
      inverseCumulativeProbability in interface DiscreteDistribution
      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0).

    • sample

      public static int[] sample​(int n, DiscreteDistribution.Sampler sampler)
      Utility function for allocating an array and filling it with n samples generated by the given sampler.
      Parameters:
      n - Number of samples.
      sampler - Sampler.
      Returns:
      an array of size n.