{"title":"对称多元密度函数的分解","authors":"Kiyotaka Iki, Kouji Tahata, S. Tomizawa","doi":"10.55937/sut/1360240217","DOIUrl":null,"url":null,"abstract":"For a T-variate density function, the present article denes the quasi-symmetry of order k (< T) and the marginal symmetry of order k, and gives the theorem that the density function is T-variate permutation symmetric if and only if it is quasi-symmetric and marginal symmetric of order k. The theorem is illustrated for the multivariate normal density function. AMS 2010 Mathematics Subject Classication. 62H17.","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"57 2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Decomposition of symmetric multivariate density function\",\"authors\":\"Kiyotaka Iki, Kouji Tahata, S. Tomizawa\",\"doi\":\"10.55937/sut/1360240217\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a T-variate density function, the present article denes the quasi-symmetry of order k (< T) and the marginal symmetry of order k, and gives the theorem that the density function is T-variate permutation symmetric if and only if it is quasi-symmetric and marginal symmetric of order k. The theorem is illustrated for the multivariate normal density function. AMS 2010 Mathematics Subject Classication. 62H17.\",\"PeriodicalId\":38708,\"journal\":{\"name\":\"SUT Journal of Mathematics\",\"volume\":\"57 2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SUT Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55937/sut/1360240217\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SUT Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55937/sut/1360240217","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Decomposition of symmetric multivariate density function
For a T-variate density function, the present article denes the quasi-symmetry of order k (< T) and the marginal symmetry of order k, and gives the theorem that the density function is T-variate permutation symmetric if and only if it is quasi-symmetric and marginal symmetric of order k. The theorem is illustrated for the multivariate normal density function. AMS 2010 Mathematics Subject Classication. 62H17.