The Ewens Sampling Formula

Simon Tavaré

W.J. Ewens


Encyclopedia of Statistical Sciences Update Volume 2.
Eds. S. Kotz, C.B. Read, D.L. Banks, pp. 230-234, 1998. Wiley New York.

Abstract

The Ewens Sampling Formula (ESF) describes a specific probability for the partition of a positive integer into parts. The distribution contains one parameter, usually denoted by theta. For the case theta=1 the distribution is quite old, going back in effect to Cauchy, since it then describes the partition into cycles of a random permutation, each possible permutation being equally likely. As noted below, the distribution arises for a much wider variety of combinatorial objects besides permutations, as well as in a variety of scientific disciplines.

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