{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T15:42:29Z","timestamp":1707925349231},"reference-count":4,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":5397,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The Ewens sampling formula is a family of probability distributions over the space of cycle types of permutations of<jats:italic>n<\/jats:italic>objects, indexed by a real parameter \u03b8. In the case \u03b8 = 1, where the distribution reduces to that induced by the uniform distribution on all permutations, the joint distributions of the numbers of cycles of lengths less than<jats:italic>b = o(n)<\/jats:italic>is extremely well approximated by a product of Poisson distributions, having mean 1\/<jats:italic>j<\/jats:italic>for cycle length<jats:italic>j<\/jats:italic>: the error is super\u2010exponentially small with<jats:italic>nb<\/jats:italic><jats:sup>\u22121<\/jats:sup>. For \u03b8 \u2260 1. the analogous approximation, with means adjusted to \u03b8\/<jats:italic>j<\/jats:italic>, is good, but with error only linear in<jats:italic>n<\/jats:italic><jats:sup>\u22121<\/jats:sup><jats:italic>b<\/jats:italic>. In this article, it is shown that, by choosing the means of the Poisson distributions more carefully, an error quadratic in<jats:italic>n<\/jats:italic><jats:sup>\u22121<\/jats:sup><jats:italic>b<\/jats:italic>can be achieved, and that essentially nothing better is possible.<\/jats:p>","DOI":"10.1002\/rsa.3240030306","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T18:29:30Z","timestamp":1180204170000},"page":"267-276","source":"Crossref","is-referenced-by-count":2,"title":["Refined Approximations for the Ewens Sampling Formula"],"prefix":"10.1002","volume":"3","author":[{"given":"A. D.","family":"Barbour","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"R.ArratiaandS.Tavar\u00e9 The cycle structure of random permutations Ann. Probab.(1991).","DOI":"10.1214\/aop\/1176989707"},{"key":"e_1_2_1_3_2","unstructured":"R.Arratia A. D.Barbour andS.Tavar\u00e9 Poisson process approximations for the Ewens sampling formula (submitted)."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522355.001.0001","volume-title":"Poisson Approximation","author":"Barbour A. D.","year":"1992"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","first-page":"463","DOI":"10.2307\/1426228","article-title":"The sampling theory of selectively neutral alleles","volume":"6","author":"Watterson G. A.","year":"1974","journal-title":"Adv. Appl. Probab."}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240030306","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240030306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T15:27:40Z","timestamp":1707924460000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240030306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/rsa.3240030306"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240030306","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}