Estimation and Prediction for a Progressively First-Failure Censored Inverted Exponentiated Rayleigh Distribution

Abstract

We discuss inverted exponentiated Rayleigh distribution under progressive first-failure censoring. Maximum likelihood and Bayes estimates of unknown parameters are obtained. An expectation–maximization algorithm is used for computing maximum likelihood estimates. Asymptotic intervals are constructed from the observed Fisher information matrix. Bayes estimates of unknown parameters are obtained under the squared error loss function. We construct highest posterior density intervals based on importance sampling. Different predictors and prediction intervals of censored observations are discussed. A Monte Carlo simulations study is performed to compare different methods. Finally, three real data sets are analyzed for illustration purposes.