Estimating the parameters of an exponentiated inverted Weibull distribution under type-II censoring

Abstract

The exponentiated inverted Weibull distribution is a generalization of the exponentiated inverted exponential distribution as well as the inverted Weibull distribution. In this paper, Bayes and classical estimators have been obtained for two parameters exponentiated inverted Weibull distribution when sample is available from complete and type II censoring scheme. Several Bayesian estimates are obtained against different symmetric and asymmetric loss functions such as squared error and LINEX. This was done with respect to the conjugate priors for two shape parameters. As expected, when the shape parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We used an approximation based on the Lindley and Markov chain Monte Carlo method (MCMC) methods for obtaining Bayes estimates under these loss functions. All Bayesian estimates are compared with the corresponding maximum likelihood estimates numerically in terms of their mean square error values. Finally, real data sets are analyzed for the purpose of illustration.