{"title":"Remarks on the Papers by Coelho-Barros et al. (2017), Usman et al. (2021) and Obeid and Kadry (2022)","authors":"G. Hamedani, I. Ghosh, A. Saghir","doi":"10.18187/pjsor.v18i3.4180","DOIUrl":null,"url":null,"abstract":"We would like to point out that the formula for the cumulative distribution given in Coelho-Barros et al. (2017) and a similar version of it given in Usman et al. (2021) are not cumulative distribution functions as these functions do not satisfy the one or more necessary and sufficient conditions for a function to be a cumulative distribution function. We would also like to mention that formulas for the cumulative distribution functions of product and ratio of two independent Pareto and Exponential random variables given by Obeid and Kadry (2022) are not cumulative distribution functions either. We do not believe that these formulas can be fixed to be cumulative distribution functions. In this short article, we provide mathematical justification in support of these claims.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pakistan Journal of Statistics and Operation Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18187/pjsor.v18i3.4180","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We would like to point out that the formula for the cumulative distribution given in Coelho-Barros et al. (2017) and a similar version of it given in Usman et al. (2021) are not cumulative distribution functions as these functions do not satisfy the one or more necessary and sufficient conditions for a function to be a cumulative distribution function. We would also like to mention that formulas for the cumulative distribution functions of product and ratio of two independent Pareto and Exponential random variables given by Obeid and Kadry (2022) are not cumulative distribution functions either. We do not believe that these formulas can be fixed to be cumulative distribution functions. In this short article, we provide mathematical justification in support of these claims.
期刊介绍：
Pakistan Journal of Statistics and Operation Research. PJSOR is a peer-reviewed journal, published four times a year. PJSOR publishes refereed research articles and studies that describe the latest research and developments in the area of statistics, operation research and actuarial statistics.
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