{"title":"Some new results on the Rényi quantile entropy Ordering","authors":"Lei Yan , Dian-tong Kang","doi":"10.1016/j.stamet.2016.04.003","DOIUrl":null,"url":null,"abstract":"<div><p>Rényi (1961) proposed the Rényi entropy. Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the residual entropy. Recently, Nanda et al. (2014) obtained a quantile<span><span> version of the Rényi residual entropy, the Rényi residual quantile entropy (RRQE). Based on the RRQE function, they defined a new stochastic order, the Rényi quantile entropy (RQE) order, and studied some properties of this order. In this paper, we focus on further properties of this new order. Some characterizations of the RQE 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 RQE order in several </span>stochastic models are discussed.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"33 ","pages":"Pages 55-70"},"PeriodicalIF":0.0000,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2016.04.003","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S157231271630003X","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: 7
Abstract
Rényi (1961) proposed the Rényi entropy. Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the residual entropy. Recently, Nanda et al. (2014) obtained a quantile version of the Rényi residual entropy, the Rényi residual quantile entropy (RRQE). Based on the RRQE function, they defined a new stochastic order, the Rényi quantile entropy (RQE) order, and studied some properties of this order. In this paper, we focus on further properties of this new order. Some characterizations of the RQE 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 RQE order in several stochastic models are discussed.
rsamunyi(1961)提出了rsamunyi熵。Ebrahimi and Pellerey(1995)和Ebrahimi(1996)提出残差熵。最近，Nanda et al.(2014)获得了一种分位数版本的r残差熵，r残差分位数熵(RRQE)。在RRQE函数的基础上，他们定义了一种新的随机阶数——r分位熵(RQE)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RQE序列的一些特征，得到了闭包和反闭包性质，并给出了一些示例。作为一个主要结果的应用，讨论了几种随机模型中RQE阶的保持问题。
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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