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On Generating T-X Family of Pareto-Exponential Distribution with Properties and Applications

Noor Waseem, Shakila Bashir


The Pareto distribution plays an important role in the theory and application of statistics. We introduced a new family of continuous distribution generating from Pareto random variable called the Pareto-X family or T-X family of Pareto–Exponential (PE) distribution. Various mathematical properties including L-moments, mean deviation, moment generating function (MGF), cumulative generating function, characteristic function and quantile function of the Pareto-Exponential distribution have been derived. To check the reliability of a system some reliability measures as reliability function, hazard rate, cumulative hazard rate, reversed hazard rate and mean residuals lifetime have also been discussed. Lorenz and Bonferroni curves, Renyi, Q and Shannon entropies have been determined to measure the inequality and uncertainty. The expression of order statistics from the new distribution is derived. Parameters for the proposed model are estimated by maximum likelihood estimation (MLE) and method of moments (MOM). A real-life data is applied to illustrate the comparison of the new distribution with the existing distributions in the literature.


Exponential Pareto distribution, PE, L-moments, MGF, Order statistics, MOM.

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