Bayesian Estimation for the Scale Parameter of a Family of Lifetime Distributions under Different Priors

Abstract

In this study, the Bayes estimators for the scale parameter of a family of lifetime distributions are considered under the assumptions of non-informative and conjugate priors. The uniform and inverted gamma priors are observed to obtain the posterior distribution for the scale parameter of this family of lifetime distributions. Considerations are given to three loss functions, namely, Squared Error Loss Function (SELF), Quadratic Loss Function (QLF) and Precautionary Loss Function (PLF). The performance of the estimator is assessed on the basis of its relative posterior risk. Markov Chain Monte Carlo (MCMC) Simulation Techniques are used to compare the performance of these estimators.