Thesis (M.Sc.) - Cairo University - Institute of Statistical Studies and Research - Department of Mathematical Statistics

Of interest to us here is the (P-A-L) extension suggested by Pappas, Adamidis and Loukas (2012). This thesis consists of four chapters including this introductory one. Chapter 2 is devoted to some basic de_nitions, notations and basic concepts that are used throughout the thesis. The basic statistical properties, some useful functions and some im- portant statistical distributions are presented. Estimation problem is also considered in view of maximum likelihood. Chapter 3 is devoted to literature review for the (P-A-L) method and review some distributions based on (P-A-L) method. Our aim in chapter 4 is to introduce new distribution, with four parameters Ü, Ý, Þ and p, called (P-A-L)-Modified Weibull distribution. The cumulative distribution function (cdf), probability density function (pdf) and survival function for the distribution are illustrated. The hazard function is also illustrated. Simulation study is used to check the performance of the accuracy of point and interval estimates parameters. Finally, real data set used to show the applicability the distribution

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