التقدير البيزي لدالة المعولية لتوزيع دالة القوة تحت دوال خسارة مختلفة.

Abstract

The Power function distribution has been widely used especially in the modeling of life time data .It provides a statistical model which has a wide variety of application in many areas .The conventional maximum likelihood method is the usual way to estimate the parameters of a probability distribution. Bayesian approach that depends on symmetric loss function “quadratic” and asymmetric loss function “precautionary ,logarithmic and linex” has received much attention in contention with other estimation methods. In this paper we explore and compare the performance of the maximum likelihood estimates with the Bayesian estimate of Reliability function for the two parameter Power function distribution. The maximum likelihood estimation, Bayesian using Jeffrey prior, for estimating the Reliability function of life time are presented. We explore the performance of these estimators numerically under varying conditions. Through the simulation study a comparison are made on the performance of these estimators with respect to the mean square error (MSE). Based on the results of this simulation study the Bayesian approach depends on logarithmic loss function used in the estimating of reliability function of the two parameter power function distribution is found to be superior compared to the conventional methods with respect to MSE values.