{"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":null,"pages":null},"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}
引用次数: 4
Abstract
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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