{"title":"On Cumulative Residual Renyi's Entropy","authors":"V. Zardasht","doi":"10.15446/rce.v45n2.96844","DOIUrl":null,"url":null,"abstract":"At the entropy measures and their generalization path, in the direction of statistics and information science, recently, Sunoj & Linu (2012) proposed the cumulative residual Renyi's entropy of order α and its dynamic version and studied its main properties. In this paper, we introduce an alternative measure of cumulative residual Renyi's entropy (CRRE) of order α which, unlike the mentioned one, is positive for all distributions and all values of α. We also consider its dynamic version and study their main properties in the context of reliability theory and stochastic orders. We give an estimator of the proposed CRRE and investigate its exact and asymptotic distribution. Numerous examples illustrating the theory are also given.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Colombiana De Estadistica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15446/rce.v45n2.96844","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
At the entropy measures and their generalization path, in the direction of statistics and information science, recently, Sunoj & Linu (2012) proposed the cumulative residual Renyi's entropy of order α and its dynamic version and studied its main properties. In this paper, we introduce an alternative measure of cumulative residual Renyi's entropy (CRRE) of order α which, unlike the mentioned one, is positive for all distributions and all values of α. We also consider its dynamic version and study their main properties in the context of reliability theory and stochastic orders. We give an estimator of the proposed CRRE and investigate its exact and asymptotic distribution. Numerous examples illustrating the theory are also given.
期刊介绍：
The Colombian Journal of Statistics publishes original articles of theoretical, methodological and educational kind in any branch of Statistics. Purely theoretical papers should include illustration of the techniques presented with real data or at least simulation experiments in order to verify the usefulness of the contents presented. Informative articles of high quality methodologies or statistical techniques applied in different fields of knowledge are also considered. Only articles in English language are considered for publication.
The Editorial Committee assumes that the works submitted for evaluation
have not been previously published and are not being given simultaneously for publication elsewhere, and will not be without prior consent of the Committee, unless, as a result of the assessment, decides not publish in the journal. It is further assumed that when the authors deliver a document for publication in the Colombian Journal of Statistics, they know the above conditions and agree with them.
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