Constructing an Extended Weighted Probability Distribution to Estimate the Failure Function
With Practical Application
A thesis submitted to the council of the college of Administration &Economics\ University of Karbala as partial fulfillment of the requirements for the degree of Master of Statistics Sciences

By
Nahla Hadi Abdul-Sahib
Under supervision
Prof. Dr . Mahdi Wahab Nea’ama Naser Allah

Abstract

We introduce a new distribution is called the extended weighted fréchet distribution which we obtain by applying Azalini’s method deriving the probability density function (pdf) and the probability cumulative function (CDF) and then it is deduced some statistical properties such as mean , variance , coefficients of variation, coefficient of skewedness and coefficient of kurtosis and mode. The parameters (l,q,a) and failure function of the new distribution were estimated by the following estimation methods : Maximum Likelihood Method (MLE), maximum product of spacing (PSM), Cramer-Von Mises Minimum (CVM) and Percentiles Estimator methods (Per). We used The monte Carlo simulation to compare the performances of the proposed estimators obtained through methods of estimation Depending on the comparison of the mean square error (MSE) by Ranks method for samples size (35, 20, 15, 10).

From the simulation results, it was found that the Maximum product spacing method is the best method for estimating at a sample size of 35 and with assumed values ).

As for the application side, it includes readings for the failure time of the cutting tool sample in the turning machine. It ensures a comparison between the Frechet distribution and new the expanded weight Frechet distribution of best for estimating the failure function as well as determining the failure function of the cutting tool at the specified conditions for the cutting process after the coating process.