Bayesian Approach of Estimating Shape Parameter of Log Logistic Distribution

Abstract

In this research, Log logistic distribution under Bayesian paradigm is studied. Posterior distribution has been derived using Uniform and Jeffrey’s’ priors. The three loss functions taken up are squared error loss function (SELF), weighted balanced loss function (WBLF) and precautionary loss function (PLF). The performance of an estimator is assessed on the basis of its relative posterior risk. An extensive simulation was carried out to illustrate the applicability of this research and to compare the performance of different estimators. The study indicated that for estimation of the shape parameter using Bayesian estimation technique, the precautionary loss function can effectively be employed.

Keywords: Bayesian estimation, Log logistic distribution, Uniform prior, Jeffrey’s prior, loss functions.