{"title":"Simulation algorithms for hierarchical Archimedean copulas beyond the completely monotone case","authors":"Jan-Frederik Mai","doi":"10.1515/demo-2019-0010","DOIUrl":null,"url":null,"abstract":"Abstract Two simulation algorithms for hierarchical Archimedean copulas in the case when intra-group generators are not necessarily completely monotone are presented. Both generalize existing algorithms for the completely monotone case. The underlying stochastic models for both algorithms arise as a particular instance of a more general probability space studied recently in Ressel, P. (2018): A multivariate version of Williamson’s theorem, ℓ1-symmetric survival functions, and generalized Archimedean copulas. Depend. Model. 6, 356–368. On this probability space the inter-group dependence need not be Archimedean, however, we highlight two particular circumstances that guarantee that a hierarchical Archimedean copula is obtained.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"7 1","pages":"202 - 214"},"PeriodicalIF":0.8000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2019-0010","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dependence Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/demo-2019-0010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract Two simulation algorithms for hierarchical Archimedean copulas in the case when intra-group generators are not necessarily completely monotone are presented. Both generalize existing algorithms for the completely monotone case. The underlying stochastic models for both algorithms arise as a particular instance of a more general probability space studied recently in Ressel, P. (2018): A multivariate version of Williamson’s theorem, ℓ1-symmetric survival functions, and generalized Archimedean copulas. Depend. Model. 6, 356–368. On this probability space the inter-group dependence need not be Archimedean, however, we highlight two particular circumstances that guarantee that a hierarchical Archimedean copula is obtained.
期刊介绍：
The journal Dependence Modeling aims at providing a medium for exchanging results and ideas in the area of multivariate dependence modeling. It is an open access fully peer-reviewed journal providing the readers with free, instant, and permanent access to all content worldwide. Dependence Modeling is listed by Web of Science (Emerging Sources Citation Index), Scopus, MathSciNet and Zentralblatt Math. The journal presents different types of articles: -"Research Articles" on fundamental theoretical aspects, as well as on significant applications in science, engineering, economics, finance, insurance and other fields. -"Review Articles" which present the existing literature on the specific topic from new perspectives. -"Interview articles" limited to two papers per year, covering interviews with milestone personalities in the field of Dependence Modeling. The journal topics include (but are not limited to): -Copula methods -Multivariate distributions -Estimation and goodness-of-fit tests -Measures of association -Quantitative risk management -Risk measures and stochastic orders -Time series -Environmental sciences -Computational methods and software -Extreme-value theory -Limit laws -Mass Transportations
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