ZipfianDistribution Class

public class ZipfianDistribution : DiscreteDistribution

Public Class ZipfianDistribution
	Inherits DiscreteDistribution

public ref class ZipfianDistribution : public DiscreteDistribution

type ZipfianDistribution = 
    class
        inherit DiscreteDistribution
    end

Inheritance

Object  →  Distribution  →  DiscreteDistribution  →  ZipfianDistribution

The Zipfian distribution is a discrete probability distribution commonly used to model the frequency of events in a large dataset, where the frequency of an event is inversely proportional to its rank.

The distribution is characterized by two parameters: a shape parameter s > 0 which controls the skewness of the distribution, and a parameter N > 0 which represents the number of elements in the distribution. The probability mass function is given by p(k) = k^(-s) / H(N,s), where H(N,s) is the Nth generalized harmonic number of order s.

When the shape parameter s is high, the distribution is heavily skewed toward the lower ranks. As s approaches 0, the distribution becomes more uniform. When the second (integer) parameter N approaches infinity, the Zipfian distribution approaches a ZipfDistribution.

The Zipfian distribution has applications in many fields including linguistics (modeling word frequencies in natural languages), information retrieval, population distributions in cities, income distributions, and web traffic modeling. It is commonly used in performance testing to generate realistic access patterns for caches, databases, and other systems where some items are accessed much more frequently than others.

Reference