Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22710
Arratia, R; Barbour, A D; Tavaré, S (1992). Poisson process approximations for the Ewens sampling formula. Annals of Applied Probability, 2(3):519-535.
The Ewens sampling formula is a family of measures on permutations, that arises in population genetics, Bayesian statistics and many other applications. This family is indexed by a parameter ; the usual uniform measure is included as the special case . Under the Ewens sampling formula with parameter , the process of cycle counts converges to a Poisson process with independent coordinates and . Exploiting a particular coupling, we give simple explicit upper bounds for the Wasserstein and total variation distances between the laws of and . This Poisson approximation can be used to give simple proofs of limit theorems with bounds for a wide variety of functionals of such random permutations.
|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Uncontrolled Keywords:||Total variation; population genetics; permutations|
|Deposited On:||12 Apr 2010 12:30|
|Last Modified:||23 Nov 2012 13:26|
|Publisher:||Institute of Mathematical Statistics|
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