{"title":"Quantile dependence: A generalization of upper and lower tail dependence","authors":"Ali Dastbaravarde, Ali Dolati","doi":"10.1016/j.fss.2024.109165","DOIUrl":null,"url":null,"abstract":"<div><div>A popular measure of association is the tail dependence coefficient, which measures the strength of dependence in the tail of a bivariate distribution. In this paper, we introduce the concept of quantile dependence, which extends the idea of tail dependence and can be used to measure the dependence of specific quantiles of two random variables in a particular area of the distribution's domain. We analyze the characteristics of the proposed quantile dependence coefficient and provide various examples to demonstrate our findings.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109165"},"PeriodicalIF":3.2000,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165011424003117","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
A popular measure of association is the tail dependence coefficient, which measures the strength of dependence in the tail of a bivariate distribution. In this paper, we introduce the concept of quantile dependence, which extends the idea of tail dependence and can be used to measure the dependence of specific quantiles of two random variables in a particular area of the distribution's domain. We analyze the characteristics of the proposed quantile dependence coefficient and provide various examples to demonstrate our findings.
期刊介绍：
Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies.
In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.
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