Bayesian Inference for Logarithmic Transformed Exponential Distribution in Presence of Adaptive Progressive Type-II Censoring

Abstract

In this paper, estimations problem (point and interval) are studied for the logarithmic transformed exponential (LTE) distribution based on an adaptive progressive Type-II (APTII ) censoring scheme. In point estimation; the maximum likelihood estimate (MLE) and Bayesian estimates (BE) based on squared error and Linex loss functions are obtained. The Markov Chain Monte Carlo (MCMC) technique is used to compute Bayes estimates by using gamma prior for the unknown parameter under two different loss functions. Metropolis-Hasting (M-H) algorithm has been applied to generate MCMC samples from the posterior density. In case of interval estimation; asymptotic confidence interval (CI) and two different bootstrap CI’s namely; Boot-p and Boot-t are obtained. Also, we have computed posterior credible interval for the unknown parameter. The performance of these estimates are studied on the basis of their risks. Finally, a real dataset has been taken for different censoring schemes and times under APTII censoring.