Bayesian Inference on General-Order Statistic Models

Abstract

In the present article, we consider the Bayesian inference of the unknown population size N , along with the other model parameters based on a general order statistics model. The inference is carried out for (i) exponential, (ii) Weibull, and (iii) generalized exponential lifetime distributions. It is observed that under the standard squared error loss function, the Bayes estimators cannot be obtained explicitly. The Bayes estimator of N and its credible interval are obtained using the Markov Chain Monte Carlo technique. The Bayesian methods can be implemented very easily and it avoids the difficulties of the classical inference. In this case, there is a positive probability that the maximum likelihood estimator of N is not finite. An extensive Monte Carlo simulation experiments have been performed to observe the behavior of the proposed Bayesian method. The Bayes factors and the predictive likelihood values have been used for choosing the correct model. The analysis of one real data set has been performed to illustrate the proposed method.