{"title":"关于LQE排序的一些新结果","authors":"Dian-tong Kang","doi":"10.1016/j.stamet.2016.06.001","DOIUrl":null,"url":null,"abstract":"<div><p>Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the residual entropy. Recently, Sunoj and Sankaran (2012) obtained a quantile<span><span> version of the residual entropy, the residual quantile entropy (RQE). Based on the RQE function, they defined a new stochastic order, the less quantile entropy (LQE) order, and studied some properties of this order. In this paper, we focus on further properties of this new order. Some characterizations of the LQE order are investigated, closure and reversed closure properties are obtained, meanwhile, some illustrative examples are shown. As applications of a main result, the preservation of the LQE order in several </span>stochastic models is discussed. We give the closure and reversed closure properties of the LQE order for coherent systems with dependent and identically distributed components, and also consider a potential application to insurance of this order.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"32 ","pages":"Pages 218-235"},"PeriodicalIF":0.0000,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2016.06.001","citationCount":"4","resultStr":"{\"title\":\"Some new results on the LQE ordering\",\"authors\":\"Dian-tong Kang\",\"doi\":\"10.1016/j.stamet.2016.06.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the residual entropy. Recently, Sunoj and Sankaran (2012) obtained a quantile<span><span> version of the residual entropy, the residual quantile entropy (RQE). Based on the RQE function, they defined a new stochastic order, the less quantile entropy (LQE) order, and studied some properties of this order. In this paper, we focus on further properties of this new order. Some characterizations of the LQE order are investigated, closure and reversed closure properties are obtained, meanwhile, some illustrative examples are shown. As applications of a main result, the preservation of the LQE order in several </span>stochastic models is discussed. We give the closure and reversed closure properties of the LQE order for coherent systems with dependent and identically distributed components, and also consider a potential application to insurance of this order.</span></p></div>\",\"PeriodicalId\":48877,\"journal\":{\"name\":\"Statistical Methodology\",\"volume\":\"32 \",\"pages\":\"Pages 218-235\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.stamet.2016.06.001\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistical Methodology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1572312716300120\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572312716300120","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 4
摘要
Ebrahimi and Pellerey(1995)和Ebrahimi(1996)提出残差熵。最近，Sunoj和Sankaran(2012)获得了残差熵的分位数版本，残差分位数熵(residual quantile entropy, RQE)。在RQE函数的基础上，他们定义了一种新的随机阶数——少分位熵(LQE)阶数，并研究了该阶数的一些性质。在本文中，我们重点讨论了这一新阶的进一步性质。研究了LQE阶的一些性质，得到了闭包和反闭包性质，并给出了一些例子。作为一个主要结果的应用，讨论了几种随机模型中LQE阶的保持问题。我们给出了具有依赖和相同分布组件的相干系统的LQE阶的闭包和反闭包性质，并考虑了该阶的保险的潜在应用。
Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the residual entropy. Recently, Sunoj and Sankaran (2012) obtained a quantile version of the residual entropy, the residual quantile entropy (RQE). Based on the RQE function, they defined a new stochastic order, the less quantile entropy (LQE) order, and studied some properties of this order. In this paper, we focus on further properties of this new order. Some characterizations of the LQE order are investigated, closure and reversed closure properties are obtained, meanwhile, some illustrative examples are shown. As applications of a main result, the preservation of the LQE order in several stochastic models is discussed. We give the closure and reversed closure properties of the LQE order for coherent systems with dependent and identically distributed components, and also consider a potential application to insurance of this order.
期刊介绍：
Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.
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