Parameter estimation of the inverted exponentiated Rayleigh distribution based on progressively first-failure censored samples

Abstract

We study statistical inference of the inverted exponentiated Rayleigh distribution under progressively first-failure censoring samples in our paper. Specifically, we deal with Maximum likelihood and Bayes estimators of parameters. The observed Fisher matrix is conducive to obtain asymptotic confidence interval. Parametric bootstrap methods are applied to provide the confidence intervals. Bayes estimators in terms of squared error loss function are derived with Metropolis–Hastings technique, which are helpful to construct highest posterior density credible intervals. We compare the behavior of various estimators by conducting Monte Carlo simulations. A set of actual data is analyzed to introduce the proposed methods.