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

ByTamara Ali Ghany

Under supervision
Ass. Prof.  Dr . Mahdi Wahab Nea’ama Naser Allah

abstract:

The interest of statisticians in recent decades has increased in addressing the case of anomalies in the data, or more precisely, how to deal with the data in the event that it contains anomalies (contaminates), in two directions, the first is the use of fortified methods from which to obtain more efficient capabilities than the usual methods in the case of The presence of contaminates, and the other direction is the Bayesian direction, or the so-called Robust Bayesian, which is the parameter or parameters to be assessed as random variables for which previous information is available in a probability distribution formula called the (prior) distribution, which depends on the estimation of Bayesian on the sensitivity of this distribution. The extent of its accuracy in determining the prior information about the parameters to be assessed.

This thesis aimed at estimating the measurement parameter for the distribution of Frechet by using the robust Bayesian  method based on the contaminant variety (contaminant ML-II-) at four types of the standard basic distribution and the main contaminant distribution which is when the standard base distribution and the standard contaminant distribution is the Weibull distribution and when the main distribution is The standard and standard pollutant distribution is the inverse Frechet distribution, and when the standard base distribution and the standard contaminates distribution is a gamma distribution, and when the standard base distribution and the standard contaminates distribution are the Lindley distribution at a squared loss function, and then the  estimation using the standard mean squared error (MSE) . Since the Monte-Carlo simulation method was used for the purpose of testing the preference of the estimation methods used in estimating the parameters of the Frigate distribution using the hippocampal Bayesian  method under the category of contamination, the ML- type II, and it was concluded that all the approved estimation methods are average closer to the default values ​​of the measurement parameter for the Freight distribution (β) when all the experiments of simulation  and sample sizes are assumed at each level of contamination (ε= 0.1,0.5,0.9). And the best robust Bayesian  estimate for the prior distribution class. The second ML was at the standard primary distribution and the contaminated primary distribution, followed by the inverse  Frechet distribution and from then the gamma distribution and finally the Weibull distribution, by increasing the value of the contamination ratios in the primary distribution (0.9-0.1), the preference for the robust Bayesian  estimation based on the standard basic class of Lindley and the main contaminant of Lindley was achieved, indicating the preference for using the primary distribution of Lindley in estimating the parameters of the Frechet distribution. The results of the analysis of applied data represented in the lifetimes of the days under treatment until death or recovery from disease or leaving the hospital for those infected with the virus (COVD-19), obtained from the Fever Department at Al-Hussein Teaching Hospital in Karbala Governorate, emphasizing the need to use the Lindley distribution as a primary distribution contaminated with certain percentages of contamination in finding an estimate of the robust Bayesian  in case the real data follow the Frechet distribution.

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