{"title":"与偶数抽样公式相关的不同分量数的埃奇沃斯展开式","authors":"Hajime Yamato","doi":"10.14490/JJSS.43.17","DOIUrl":null,"url":null,"abstract":"The Ewens sampling formula is well-known as a distribution of a random partition of the positive integer n. For the number of distinct components of the Ewens sampling formula, we derive its Edgeworth expansion. It is different from the Edgeworth expansion for the sum of independent and identicallydistributed random variables. It contains the digamma function of the parameter of the Ewens sampling formula. Especially, for the random permutation, the Edgeworth expansion contains Euler’s constant. The Edgeworth expansion is examined numericallyusing its graph.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"76 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"EDGEWORTH EXPANSIONS FOR THE NUMBER OF DISTINCT COMPONENTS ASSOCIATED WITH THE EWENS SAMPLING FORMULA\",\"authors\":\"Hajime Yamato\",\"doi\":\"10.14490/JJSS.43.17\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Ewens sampling formula is well-known as a distribution of a random partition of the positive integer n. For the number of distinct components of the Ewens sampling formula, we derive its Edgeworth expansion. It is different from the Edgeworth expansion for the sum of independent and identicallydistributed random variables. It contains the digamma function of the parameter of the Ewens sampling formula. Especially, for the random permutation, the Edgeworth expansion contains Euler’s constant. The Edgeworth expansion is examined numericallyusing its graph.\",\"PeriodicalId\":326924,\"journal\":{\"name\":\"Journal of the Japan Statistical Society. Japanese issue\",\"volume\":\"76 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Japan Statistical Society. Japanese issue\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14490/JJSS.43.17\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Japan Statistical Society. Japanese issue","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14490/JJSS.43.17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
EDGEWORTH EXPANSIONS FOR THE NUMBER OF DISTINCT COMPONENTS ASSOCIATED WITH THE EWENS SAMPLING FORMULA
The Ewens sampling formula is well-known as a distribution of a random partition of the positive integer n. For the number of distinct components of the Ewens sampling formula, we derive its Edgeworth expansion. It is different from the Edgeworth expansion for the sum of independent and identicallydistributed random variables. It contains the digamma function of the parameter of the Ewens sampling formula. Especially, for the random permutation, the Edgeworth expansion contains Euler’s constant. The Edgeworth expansion is examined numericallyusing its graph.
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