Zero Truncated Poisson - Pareto Distribution: Application and Estimation Methods

137c5f56-4ad4-457d-ae9e-36c76891c97220230216045706632wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=4051919202291920222210.37394/23206.2023.22https://wseas.com/journals/mathematics/2023.phpZero Truncated Poisson - Pareto Distribution: Application and Estimation MethodsAbdallah M. MBadrAdministration Depart-Business College, King Khalid University, Abha, SAUDI ARABIATamerHassanDepartment of Statistics College of commerce - Al-Azhar University, Cairo, EGYPTTarek ShamsEl DinDepartment of Data Science and Information Technology, Taiz University, YEMENFaisal. A. MAliDepartment of Data Science and Information Technology, Taiz University, YEMENThis article introduces and discusses a new three-parameter lifespan distribution called Zero-Truncated Poisson Pareto distribution ZTPP. that is built on compounding Pareto distribution as a continuous distribution and Zero-Truncated Poisson distribution as a discrete distribution. Various statistical properties and reliability characteristics of the proposed distribution have been investigated including explicit expressions for the moments, moment generating function, quantile function, and median. With three parameters, the suggested distribution has an advantage over other distributions in that it makes estimating the model parameters simpler. To estimate the unknown parameters of the ZTPP distribution, the maximum likelihood method, and L. Moments method are employed. Moreover, a real data set is used to evaluate the significance and ensure the applicability of the proposed distribution as compared to other probability distributions. The derived model proved to be the best compared to other fitted models, where the criteria values of (AIC), (CAIC), and (BIC) are minimum values by using the ZTPP distribution. The proposed model is hoped to attract a wider application.2162023216202313213816https://wseas.com/journals/mathematics/2023/a325106-005(2023).pdf10.37394/23206.2023.22.16https://wseas.com/journals/mathematics/2023/a325106-005(2023).pdf10.1007/s42519-019-0059-2G. A. S. Aguilar, F. A. Moala, and G. M. Cordeiro, “Zero-Truncated Poisson Exponentiated Gamma Distribution: Application and Estimation Methods,” J. Stat. Theory Pract., vol. 13, no. 4, pp. 1–20, 2019. 10.1016/s0167-7152(98)00012-1K. Adamidis and S. Loukas, “A lifetime distribution with decreasing failure rate,” Stat. Probab. 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