Weighted Generalized Entropy function for Double Truncated Weibull-pareto Distribution

A thesis Submitted to

College of Administration and Economic-Karbala University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics

By

Hazem Abed Al-Razaaq Abed Al-Amer

Under supervision

Prof. Dr. Mahdi Wahhab Neamah Naser Allah

Abstract

The thesis presented doubly truncated Weibull-Pareto Distribution, with three parameters (δ, θ, λ,) with a study mathematical properties and methods of estimating its parameters by using four methods of estimation, (Maximum Likelihood Method, Moment Method, Percentiles Estimators Method, and the Method of Length-biased Moment),  and aimed The thesis mainly to estimate the weighted generalized entropy function of order (α, β). to measure change of uncertainty in the Weibull-Pareto Distribution with different values of the amputation. On the experimental side, simulation using the Monte Carlo method was used to test the preference of the estimation methods,  Different values ​​were chosen for the shape parameter (δ, λ) and the scale parameter (θ) with six models, and the comparison between the estimation methods was done by using the partial and over ranks corresponding to the mean of the squares of error, the Maximum Likelihood Method showed It has the greatest advantage over the other methods because it corresponds to the lowest total of ranks, especially at large sample sizes. On the application side, the Maximum Likelihood Method was used to estimate weighted generalized entropy function of order (α, β), and study increase and decrease in this function at different values of truncation in a sample of (95) observations representing working hours Until the failure of the magnetic resonance device, of the Imam Al-Sadiq Hospital in the Health Department of Babylon, as the thesis led to results, the most important use Maximum Likelihood Method to estimate the parameters of the Weibull-Pareto Distribution doubly amputation at large sample sizes, also, the entropy function increases with the increase in truncation values, which makes the distribution more fitting of the real data and then the recommendation  to the Babylon Health Department to adopt the compound distribution Weibull-Pareto doubly amputation when studying successive  failure times for other systems