Bayesian inference and prediction for generalized inverted exponential distribution for Type-II censored data

Abstract

The manuscript introduces Bayesian estimation and prediction of a generalized version of the inverted exponential distribution for Type-II censored data. It further reflects on the Bayesian estimation of the unknown parameters under the squared error loss function, assuming that both the scale and the shape parameters of the distribution have a gamma prior and are independently distributed. Under these priors, the importance sampling technique is used to calculate Bayes estimates and the corresponding highest posterior density intervals. Bayes estimates are also computed using Lindley's approximation and the Metropolis-Hastings algorithm. Monte Carlo simulations are performed to compare the performance of the proposed Bayes estimates. This article seeks to extend the posterior predictive density of future observations, as well as construct a predictive interval with a given coverage probability. A data analysis is performed for illustrative purposes.