The New Lifetime Exponential-Pareto Distribution: Properties and Estimation

This research aims to suggest a proposal of compound probability distribution which is called the Pareto-exponential distribution using the new exponential family method. The mathematical function of the probability density and the cumulative distribution function of the new distribution (NLTE-Pa) were also derived, in addition to its properties such as (Non-centric moment, central moment, Coefficient of Skewness, Coefficient of Kurtosis, coefficient of variation and median). As well as discussing the different methods for estimating the parameters, represented by (the method of estimation Maximum Likelihood, the method of estimation by Anderson Darling and the method of least squares) through the simulation method using the Mathematica program, which concluded the preference of the method of the Maximum Likelihood.