Using the MCMC algorithm to find the Bayes estimator of Pareto distribution with two Parameters based on a balanced loss function

الملخص

Pareto's distribution is one of the most widespread failure distributions of stress and strength models and is widely used in reliability theory applications. This distribution is important in many fields, including operations research, queuing theory, communications, mechanical engineering, and economics as a model for individuals' income.

In this research, We found baysian estimator of Pareto distribution with two Parameters based on Symmetrical and asymmetrical loss functions. We have found a new estimator of Pareto distribution with two unknown Parameters using the Markov chain Monte Carlo (MCMC) based on a new balanced loss function and Conjugate Prior distributions, and to verify the efficiency of the performance of the proposed estimate, This estimate was compared with Bayes' estimations and maximum likelihood estimation using data generated from Pareto distribution with two parameters and sample size 100 based on the Mean Error Squared (MSE) scale.

The results of the comparison showed that the proposed estimate was the best of the studied estimations, since the inferences obtained for Pareto's distribution of the parameters are new results Covering all the previous results that dealt with this distribution or one of the special cases related to it and solved the problem of complex calculations that result in Bayes' inferences using Markov chain Monte Carlo (MCMC).