Package org.hipparchus.distribution.discrete

Class ZipfDistribution

    • Constructor Detail

      • ZipfDistribution

        public ZipfDistribution​(int numberOfElements,
                        double exponent)
                 throws MathIllegalArgumentException
        Create a new Zipf distribution with the given number of elements and exponent.
        Parameters:
        numberOfElements - Number of elements.
        exponent - Exponent.
        Throws:
        MathIllegalArgumentException - if numberOfElements <= 0 or exponent <= 0.

    • 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).

        Specified by:
        logProbability in interface IntegerDistribution
        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

      • 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