{"title":"重新审视多元联结函数族","authors":"Enagnon Narcisse Agbangla, Jean-François Quessy, Louis-Paul Rivest","doi":"10.1007/s10463-025-00931-2","DOIUrl":null,"url":null,"abstract":"<div><p>This article sheds new lights on the family of multivariate beta copulas that arises as the dependence structures of the multivariate generalized beta distribution of the second type. In particular, simple formulas for the computation of Kendall’s measure of association are derived and the asymmetry properties are investigated. Also, the multivariate extreme-value attractor of the beta copula is identified and it is shown that the beta family is closed under conditioning and belongs to the class of one-factor copulas. The sampling properties of the rank-based maximum-likelihood estimator are investigated with simulations and the usefulness of the beta copulas for the modeling of multivariate datasets is illustrated on triathlon data.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 5","pages":"757 - 786"},"PeriodicalIF":0.6000,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The family of multivariate beta copulas revisited\",\"authors\":\"Enagnon Narcisse Agbangla, Jean-François Quessy, Louis-Paul Rivest\",\"doi\":\"10.1007/s10463-025-00931-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This article sheds new lights on the family of multivariate beta copulas that arises as the dependence structures of the multivariate generalized beta distribution of the second type. In particular, simple formulas for the computation of Kendall’s measure of association are derived and the asymmetry properties are investigated. Also, the multivariate extreme-value attractor of the beta copula is identified and it is shown that the beta family is closed under conditioning and belongs to the class of one-factor copulas. The sampling properties of the rank-based maximum-likelihood estimator are investigated with simulations and the usefulness of the beta copulas for the modeling of multivariate datasets is illustrated on triathlon data.</p></div>\",\"PeriodicalId\":55511,\"journal\":{\"name\":\"Annals of the Institute of Statistical Mathematics\",\"volume\":\"77 5\",\"pages\":\"757 - 786\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2025-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of the Institute of Statistical Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10463-025-00931-2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of the Institute of Statistical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10463-025-00931-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
This article sheds new lights on the family of multivariate beta copulas that arises as the dependence structures of the multivariate generalized beta distribution of the second type. In particular, simple formulas for the computation of Kendall’s measure of association are derived and the asymmetry properties are investigated. Also, the multivariate extreme-value attractor of the beta copula is identified and it is shown that the beta family is closed under conditioning and belongs to the class of one-factor copulas. The sampling properties of the rank-based maximum-likelihood estimator are investigated with simulations and the usefulness of the beta copulas for the modeling of multivariate datasets is illustrated on triathlon data.
期刊介绍：
Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
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