{"title":"矩阵变量林德利分布及其应用","authors":"Mariem Tounsi, Mouna Zitouni","doi":"10.1214/21-bjps504","DOIUrl":null,"url":null,"abstract":"Abstract. Restring on the fact that the definition of multivariate analogs of the real gamma distribution is replaced by the Wishart distribution on symmetric matrices, and based on the notion of mixture models which is a flexible and powerful tool for treating data taken from multiple subpopulations, we set forward a multivariate analog of the real Lindley distributions of the first and second kinds on the modern framework of symmetric cones which can be used to model waiting and survival times matrix data. Within this framework, we first construct a new probability distributions, named the matrix-variate Lindley distributions. Some fundamental properties of these new distributions are established. Their statistical properties including moments, the coefficient of variation, skewness and the kurtosis are discussed. We then create an iterative hybrid Expectation-Maximization Fisher-Scoring (EM-FS) algorithm to estimate the parameters of the new class of probability distributions. Through simulation as well as comparative studies with respect to the Wishart distribution, the effectiveness and reliability of the proposed distributions are proved. Finally, the usefulness and the applicability of the new models are elaborated and illustrated by means of two real data sets from biological sciences and medical image segmentation which is one of the most important and popular tasks in medical image analysis.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Matrix-variate Lindley distributions and its applications\",\"authors\":\"Mariem Tounsi, Mouna Zitouni\",\"doi\":\"10.1214/21-bjps504\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. Restring on the fact that the definition of multivariate analogs of the real gamma distribution is replaced by the Wishart distribution on symmetric matrices, and based on the notion of mixture models which is a flexible and powerful tool for treating data taken from multiple subpopulations, we set forward a multivariate analog of the real Lindley distributions of the first and second kinds on the modern framework of symmetric cones which can be used to model waiting and survival times matrix data. Within this framework, we first construct a new probability distributions, named the matrix-variate Lindley distributions. Some fundamental properties of these new distributions are established. Their statistical properties including moments, the coefficient of variation, skewness and the kurtosis are discussed. We then create an iterative hybrid Expectation-Maximization Fisher-Scoring (EM-FS) algorithm to estimate the parameters of the new class of probability distributions. Through simulation as well as comparative studies with respect to the Wishart distribution, the effectiveness and reliability of the proposed distributions are proved. Finally, the usefulness and the applicability of the new models are elaborated and illustrated by means of two real data sets from biological sciences and medical image segmentation which is one of the most important and popular tasks in medical image analysis.\",\"PeriodicalId\":51242,\"journal\":{\"name\":\"Brazilian Journal of Probability and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Brazilian Journal of Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/21-bjps504\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/21-bjps504","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Matrix-variate Lindley distributions and its applications
Abstract. Restring on the fact that the definition of multivariate analogs of the real gamma distribution is replaced by the Wishart distribution on symmetric matrices, and based on the notion of mixture models which is a flexible and powerful tool for treating data taken from multiple subpopulations, we set forward a multivariate analog of the real Lindley distributions of the first and second kinds on the modern framework of symmetric cones which can be used to model waiting and survival times matrix data. Within this framework, we first construct a new probability distributions, named the matrix-variate Lindley distributions. Some fundamental properties of these new distributions are established. Their statistical properties including moments, the coefficient of variation, skewness and the kurtosis are discussed. We then create an iterative hybrid Expectation-Maximization Fisher-Scoring (EM-FS) algorithm to estimate the parameters of the new class of probability distributions. Through simulation as well as comparative studies with respect to the Wishart distribution, the effectiveness and reliability of the proposed distributions are proved. Finally, the usefulness and the applicability of the new models are elaborated and illustrated by means of two real data sets from biological sciences and medical image segmentation which is one of the most important and popular tasks in medical image analysis.
期刊介绍:
The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes.
More specifically, the following types of contributions will be considered:
(i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects.
(ii) Original articles developing theoretical results.
(iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it.
(iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.