Exponentiated Poisson-Power Lindley Distribution: Properties and Applications

In this article, the Exponentiated Poisson-power Lindley (EPPL) distribution, an extension of the Poisson-power Lindley (PPL) distribution, is introduced. Various properties of the EPPL distribution, including a linear representation, are studied. The method of maximum likelihood is utilized for parameter estimation, and its accuracy is validated through simulation technique. The flexibility of the proposed distribution is illustrated by considering the survival time of gastric patients. Additionally, a time-truncated acceptance sampling plan, based on the lifetime of products following the EPPL distribution is proposed. Key metrics such as minimum sample sizes, operating characteristic functions and the smallest ratios of mean life to specified are analyzed and presented. To illustrate the practical application of the proposed sampling plan in survival time data, a real data set comprising the survival times of cancer patients after a particular treatment is utilized and the effect of the treatment in the lifetime of the patients is examined based on the proposed sampling plan. In this article, both real datasets considered are survival time data from the medical field, highlighting the applicability of the newly introduced distribution in this context.