{"title":"双变量复合截断泊松伽玛分布的近似方法","authors":"Amal Alhejaili, Ateq A. Alghamedi","doi":"10.18187/pjsor.v20i2.4461","DOIUrl":null,"url":null,"abstract":"In certain situations probability computations are required for some complex distributions; like a compound distribution. This can leads to some comptational complexities. In such situations, the problem can be simplified by using some approximation techniques like the “saddle-point” approximation. In this paper, we have first proposed a compound bivariate distribution; namly the bivariate compound truncated Poisson-Gamma distribution; by compounding the zero truncated Poisson distribution with independent Gamma variates. The bivariate saddle-point approximation for the distribution function of the proposed distribution is obtained. An illustrative example for the approximate computation is given. An extensive simulatin study has been conducted to see the performance of the proposed saddle-point approximation for the distribution function of the bivariate compound truncated Poisson-Gamma distribution. It is found that the proposed saddle-point approximation is reasonably good to approximate the distribution function of the bivariate compound truncated Poisson-Gamma distribution.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximation Methods for the Bivariate Compound Truncated Poisson Gamma Distribution\",\"authors\":\"Amal Alhejaili, Ateq A. Alghamedi\",\"doi\":\"10.18187/pjsor.v20i2.4461\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In certain situations probability computations are required for some complex distributions; like a compound distribution. This can leads to some comptational complexities. In such situations, the problem can be simplified by using some approximation techniques like the “saddle-point” approximation. In this paper, we have first proposed a compound bivariate distribution; namly the bivariate compound truncated Poisson-Gamma distribution; by compounding the zero truncated Poisson distribution with independent Gamma variates. The bivariate saddle-point approximation for the distribution function of the proposed distribution is obtained. An illustrative example for the approximate computation is given. An extensive simulatin study has been conducted to see the performance of the proposed saddle-point approximation for the distribution function of the bivariate compound truncated Poisson-Gamma distribution. It is found that the proposed saddle-point approximation is reasonably good to approximate the distribution function of the bivariate compound truncated Poisson-Gamma distribution.\",\"PeriodicalId\":19973,\"journal\":{\"name\":\"Pakistan Journal of Statistics and Operation Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-06-05\",\"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.v20i2.4461\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pakistan Journal of Statistics and Operation Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18187/pjsor.v20i2.4461","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Approximation Methods for the Bivariate Compound Truncated Poisson Gamma Distribution
In certain situations probability computations are required for some complex distributions; like a compound distribution. This can leads to some comptational complexities. In such situations, the problem can be simplified by using some approximation techniques like the “saddle-point” approximation. In this paper, we have first proposed a compound bivariate distribution; namly the bivariate compound truncated Poisson-Gamma distribution; by compounding the zero truncated Poisson distribution with independent Gamma variates. The bivariate saddle-point approximation for the distribution function of the proposed distribution is obtained. An illustrative example for the approximate computation is given. An extensive simulatin study has been conducted to see the performance of the proposed saddle-point approximation for the distribution function of the bivariate compound truncated Poisson-Gamma distribution. It is found that the proposed saddle-point approximation is reasonably good to approximate the distribution function of the bivariate compound truncated Poisson-Gamma distribution.
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.