In this paper, we proposed another extension of inverse Lindley distribution, called extended inverse Lindley and studied its fundamental properties such as moments, inverse moments, mean deviation, stochastic ordering and entropy. The flexibility of the proposed distribution is shown by studying monotonicity properties of density and hazard functions. It is shown that the distribution belongs to the family of upside-down bathtub shaped distributions. Maximum likelihood estimators along with asymptotic confidence intervals are constructed for estimating the unknown parameters. An algorithm is presented for random number generation form the distribution. The property of consistency of MLEs has been verified on the basis of simulated samples. The applicability of the extended inverse Lindley distribution is illustrated by means of real data analysis.
Abstract: : In this paper, we discussed classical and Bayes estimation procedures for estimating the unknown parameters as well as the reliability and hazard functions of the flexible Weibull distribution when observed data are collected under progressively Type-II censoring scheme. The performances of the maximum likelihood and Bayes estimators are compared in terms of their mean squared errors through the simulation study. For the computation of Bayes estimates, we proposed the use of Lindley’s approximation and Markov Chain Monte Carlo (MCMC) techniques since the posteriors of the parameters are not analytically tractable. Further, we also derived the one and two sample posterior predictive densities of future samples and obtained the predictive bounds for future observations using MCMC techniques. To illustrate the discussed procedures, a set of real data is analysed.