Zero Truncated Poisson - Pareto Distribution: Application and Estimation Methods

This 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.