التقدير البيزي لدالة البقاء لتوزيع ليندلي ذو ثلاثة معلمات مع تطبيق عملي

Comparison between the standard and Expected Bayes method to estimator for the survival function for the aThree Parameter Lindely distribution by using simulation

The process of Appreciation staying function is one of the important topics that they take a huge space in the statistics researches in spite of, what is written by studies and researches about it. These studies are different according to the different methods used, which they are traditional, or Bayesian in order to get estimates of a high level of efficiency.
In this thesis we concentrate on the Al Bayesian methods to find special estimates, it’s by using the survival function, and some of its indicators of Lindely distribution whose have three tutors. It’s in the situation when we have the basic information about the tutors in the shape of potential primary function for the two shape tutors, and assessment tutor. It’s by using three of Al Bayesian methods. They are the following: the standard Bayes method, the expected Bayesian method, and hierarchical Bayesian method. These derivations appreciated methods aim to reach to the formulas that its estimates are used by a squared error loss function, and a general Entropy loss function, because of the difficult of these special mathematics processes to count estimates appreciation staying function by using Al Bayesian methods so that it is used the suggestion of scholar Lindley which is a approximately style in year (1980).
In the experimentation side we find the employment the simulation style through the use of Mont- Carlo method. It generates the random data for a sample consists of five sizes (10-25-50-75-100), which they follow Lindley distribution that it consists three tutors, and it selects supposition values for the tutors: (α.β.θ) with a nine samples, in order to get new estimates of a high accuracy. These new estimates have the characteristics that they require to be available in a perfect estimated which it’s depended on it in the approximately process, and is relied on the simulation results. it’s by the use of (IMSE) the mean of The squares of integral error statistics criterion. It’s obvious expected Bayesian method under general Entropy loss function and Hierarchical Bayesian method under, general Entropy loss function are more perfected to approximate survival function.
The study was conducted on a real sample with a size of (50) observations, representing the stay times in hours under treatment until death for those infected with the virus (CΟVD-19) which was obtained from the Fever Department at Al-Hussein Teaching Hospital in Karbala Governorate for the period between (8/5/2020) until (7/17/2020) The Bayesian prediction method and the hierarchical Bayes method were used in light of the general entropy loss function in relation to the study sample (patients CΟVD-19) the study concluded that the estimation methods usedOn the practical side, appropriate and accurate estimations are given to the study data and are consistent with what the researcher has reached on the experimental.
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