Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Mathematical Statistics

In recent few years, compound distributions arise and applied in several areas, such as public health, economics, engineering, and industrial reliability. Compounding a continuous lifetime distribution with a discrete one is a useful method for constructing flexible distributions to facilitate better modeling of lifetime data. For this purpose, De Morais (2009) introduced a new class of distributions, called Pareto power series, based on a composition of the Pareto distribution with the power-series class of discrete distributions. He also presented some general results of this class and three special cases namely ; Pareto-Poisson, Pareto-geometric and Pareto-logarithmic distributions. He showed that the Pareto distribution is a limiting special case of the Pareto power series.This thesis aims to discuss some statistical properties of the Pareto-Poisson distribution such as: quantile function, median, mode, quartiles, mean deviations, moments and moment generating function, Rényi entropy,v - entropy, mean residual life, order statistics and stress-strength reliability. Another aim is to derive the maximum likelihood, maximum product of spacings and Bayesian estimators of the unknown parameters of Pareto-Poisson distribution under complete sampling. Under the assumption of conjugate gamma priors, the Bayes estimators are developed using squared-error loss function. Using observed Fisher information matrix, two-sided approximate confidence interval estimators of the unknown parameters are constructed. Also, two numerical applications are conducted to illustrate the usefulness of proposed methods, one of them is based on simulated data and the other is based on real-life data

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