Statistical inference for the generalized inverted exponential distribution based on upper record values

In this paper, non-Bayesian and Bayesian estimators for the unknown parameters are obtained based on records from the generalized inverted exponential distribution. Bayes' estimators of the unknown parameters are obtained under symmetric and asymmetric loss functions using gamma priors on both the shape and the scale parameters. The Bayes estimators cannot be obtained in explicit forms. So we propose Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distributions and in turn computing the Bayes estimators. We have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values. Monte Carlo simulations are performed to compare the performances of the proposed methods, and a data set has been analyzed for illustrative purposes.

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