Package org.apache.commons.statistics.distribution

Class ZipfDistribution

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

Parameters: For a random variable X whose values are distributed according to this distribution, the probability mass function is given by 

   P(X = k) = H(N,s) * 1 / k^s    for k = 1,2,...,N.
H(N,s) is the normalizing constant which corresponds to the generalized harmonic number of order N of s.
  • N is the number of elements
  • s is the exponent

  • Nested Class Summary

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

    DiscreteDistribution.Sampler

  • Constructor Summary

    Constructors 
    Constructor Description
    ZipfDistribution​(int numberOfElements, double exponent)
    Creates a distribution.

  • 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 getExponent()
    Get the exponent characterizing the distribution.
    double getMean()
    Gets the mean of this distribution.
    int getNumberOfElements()
    Get the number of elements (e.g.
    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 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 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

  • Constructor Details

    • ZipfDistribution

      public ZipfDistribution​(int numberOfElements, double exponent)
      Creates a distribution.
      Parameters:
      numberOfElements - Number of elements.
      exponent - Exponent.
      Throws:
      java.lang.IllegalArgumentException - if numberOfElements <= 0 or exponent <= 0.

  • Method Details

    • getNumberOfElements

      public int getNumberOfElements()
      Get the number of elements (e.g. corpus size) for the distribution.
      Returns:
      the number of elements

    • getExponent

      public double getExponent()
      Get the exponent characterizing the distribution.
      Returns:
      the exponent

    • 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.

    • 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.

    • 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 number of elements N and exponent s, the mean is Hs1 / Hs, where
      • Hs1 = generalizedHarmonic(N, s - 1),
      • Hs = generalizedHarmonic(N, s).
      Returns:
      the mean, or Double.NaN if it is not defined.

    • getVariance

      public double getVariance()
      Gets the variance of this distribution. For number of elements N and exponent s, the mean is (Hs2 / Hs) - (Hs1^2 / Hs^2), where
      • Hs2 = generalizedHarmonic(N, s - 2),
      • Hs1 = generalizedHarmonic(N, s - 1),
      • Hs = generalizedHarmonic(N, s).
      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 always 1 no matter the parameters.
      Returns:
      lower bound of the support (always 1)

    • 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 the number of elements.
      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.