Package org.apache.commons.math3.distribution

Class ZipfDistribution

  • All Implemented Interfaces:
    java.io.Serializable, IntegerDistribution
    public class ZipfDistribution
extends AbstractIntegerDistribution
    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
    See Also:
    Zipf's law (Wikipedia), Generalized harmonic numbers, Serialized Form

    • Field Detail

      • serialVersionUID

        private static final long serialVersionUID
        Serializable version identifier.
        See Also:
        Constant Field Values

      • numberOfElements

        private final int numberOfElements
        Number of elements.

      • exponent

        private final double exponent
        Exponent parameter of the distribution.

      • numericalMean

        private double numericalMean
        Cached numerical mean

      • numericalMeanIsCalculated

        private boolean numericalMeanIsCalculated
        Whether or not the numerical mean has been calculated

      • numericalVariance

        private double numericalVariance
        Cached numerical variance

      • numericalVarianceIsCalculated

        private boolean numericalVarianceIsCalculated
        Whether or not the numerical variance has been calculated

    • Constructor Detail

      • ZipfDistribution

        public ZipfDistribution​(int numberOfElements,
                        double exponent)
        Create a new Zipf distribution with the given number of elements and exponent.

        Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see 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:
        numberOfElements - Number of elements.
        exponent - Exponent.
        Throws:
        NotStrictlyPositiveException - if numberOfElements <= 0 or exponent <= 0.

      • ZipfDistribution

        public ZipfDistribution​(RandomGenerator rng,
                        int numberOfElements,
                        double exponent)
                 throws NotStrictlyPositiveException
        Creates a Zipf distribution.
        Parameters:
        rng - Random number generator.
        numberOfElements - Number of elements.
        exponent - Exponent.
        Throws:
        NotStrictlyPositiveException - if numberOfElements <= 0 or exponent <= 0.
        Since:
        3.1

    • Method Detail

      • 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 - 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

      • 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

      • getNumericalMean

        public double getNumericalMean()
        Use this method to get the numerical value of 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

      • calculateNumericalMean

        protected double calculateNumericalMean()
        Used by getNumericalMean().
        Returns:
        the mean of this distribution

      • getNumericalVariance

        public double getNumericalVariance()
        Use this method to get the numerical value of 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 (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

      • generalizedHarmonic

        private double generalizedHarmonic​(int n,
                                   double m)
        Calculates the Nth generalized harmonic number. See Harmonic Series.
        Parameters:
        n - Term in the series to calculate (must be larger than 1)
        m - Exponent (special case m = 1 is the harmonic series).
        Returns:
        the nth generalized harmonic number.

      • 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}.

        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()
        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}.

        The upper bound of the support is the number of elements.
        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