Kouider Mohammed Ridha, Idiou Nesrine, Benatia Fatah
{"title":"ADAPTIVE ESTIMATORS OF THE GENERAL PARETO DISTRIBUTION PARAMETERS UNDER RANDOM CENSORSHIP AND APPLICATION","authors":"Kouider Mohammed Ridha, Idiou Nesrine, Benatia Fatah","doi":"10.46939/j.sci.arts-23.2-a07","DOIUrl":null,"url":null,"abstract":"In this article, we introduce adaptive estimators for parameters of the (GPD) Generalized Pareto Distribution under censored data via the KIB-estimator. The KIB-estimator is based on the Maximum Likelihood Estimates (MLE) by the exceedances over the threshold t under random censoring which was developed by [1]. Hence, it was proved that the KIB-estimator is Maximum Likelihood (ML) estimator with the uncensored case. We use the standardized MLE based on the exceedances on the uncensored situation which converge to a centered bivariate normal distribution. Whose found by [2] to standardized our adaptive KIB estimator of the GPD parameters under random censorship. As an application, we establish the asymptotic normality of an estimator of the excess-of- loss reinsurance premium for heavy-tailed distribution, through the adapted KIB estimator of GPD under censored data.","PeriodicalId":54169,"journal":{"name":"Journal of Science and Arts","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Science and Arts","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46939/j.sci.arts-23.2-a07","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we introduce adaptive estimators for parameters of the (GPD) Generalized Pareto Distribution under censored data via the KIB-estimator. The KIB-estimator is based on the Maximum Likelihood Estimates (MLE) by the exceedances over the threshold t under random censoring which was developed by [1]. Hence, it was proved that the KIB-estimator is Maximum Likelihood (ML) estimator with the uncensored case. We use the standardized MLE based on the exceedances on the uncensored situation which converge to a centered bivariate normal distribution. Whose found by [2] to standardized our adaptive KIB estimator of the GPD parameters under random censorship. As an application, we establish the asymptotic normality of an estimator of the excess-of- loss reinsurance premium for heavy-tailed distribution, through the adapted KIB estimator of GPD under censored data.