Estimation Parameters of the Frechet distribution by using shrinkage estimators with an application

A Thesis Submitted

Council of The Administration and Economics/ Karbala University as Partial fulfillment of the Requirements for the Degree of Master of Science in Statistics

 Presented by researcher

Zahra Ibrahim Abd Abbas AL-Jubouri

Supervised by

Prof. Dr. Abdulhussien Hassan Habib Al-Taee

Abstract

The Frechet distribution is one of the important statistical distributions because of what this distribution has It has many wide applications in the fields of (biological, engineering, physical and chemical). Estimating the parameters of this distribution was and still is a renewed challenge, according to the renewal of the experiences he possesses and as a result, this study came, which included estimate parameters of the Frechet distribution using Bayesian contraction estimators. The distribution parameters were estimated using four reduced Bayesian estimation methods according to loss function different (squared, LINEX, weighted and quadratic using Lindley approximation) were compared the four estimation methods based on simulation experiments (Monte-Carlo simulation) and real data. The simulation experiments included (54) different experiments according to the difference of each of (sample size, distribution parameter values and estimation method). And the comparison between different experiments based on the mean squares of error and the absolute least difference, in addition to (135) different simulation experiments to estimate the reliability function and its mean squares of error. According to the difference of (sample size, distribution parameter values and time t values), as well as different estimation method. The comparison between these experiments was done by adopting the mean of squares the error is the absolute least difference. A master’s thesis also included real data results of a size (100) watch representing the working times of the pivot sprinkler irrigation device until the malfunction, was appreciated distribution parameters and reliability function according to the four estimation methods. The results showed superior the contraction bass estimation method based on the LINEX loss function over other methods the reduced Bayesian estimate is equivalent to (57%) for the estimation of the distribution parameters and (85%) for the estimation of the reliability function. Reduced Bayesian estimation methods can be applied on other statistical distributions such as (Campbell, Kappa, and Cumaraswamy).