Zipf distribution: Difference between revisions
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Revision as of 15:03, 21 December 2008
In probability theory and statistics, the Zipf distribution and zeta distribution refer to a class of discrete probability distributions. They have been used to model the distribution of text strings and keys in databases.
The Zipf distribution with parameter n assigns probability proportional to 1/r to an integer r ≤ n and zero otherwise, with normalization factor Hn, the n-th harmonic number.
A Zipf-like distribution with parameters n and s assigns probability proportional to 1/rs to an integer r ≤ n and zero otherwise, with normalization factor .
The zeta distribution with parameter s assigns probability proportional to 1/rs to all integers r with normalization factor given by the Riemann zeta function 1/ζ(s).