Estimation and prediction for Chen distribution with bathtub shape under progressive censoring

ABSTRACT

We consider estimation of the unknown parameters of Chen distribution [Chen Z. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statist Probab Lett. 2000;49:155–161] with bathtub shape using progressive-censored samples. We obtain maximum likelihood estimates by making use of an expectation–maximization algorithm. Different Bayes estimates are derived under squared error and balanced squared error loss functions. It is observed that the associated posterior distribution appears in an intractable form. So we have used an approximation method to compute these estimates. A Metropolis–Hasting algorithm is also proposed and some more approximate Bayes estimates are obtained. Asymptotic confidence interval is constructed using observed Fisher information matrix. Bootstrap intervals are proposed as well. Sample generated from MH algorithm are further used in the construction of HPD intervals. Finally, we have obtained prediction intervals and estimates for future observations in one- and two-sample situations. A numerical study is conducted to compare the performance of proposed methods using simulations. Finally, we analyse real data sets for illustration purposes.

KEYWORDS:

• Bayesian estimation
• Bayesian prediction
• bootstrapping
• EM algorithm
• Fisherinformation matrix
• Metropolis–Hasting algorithm

Acknowledgments

Authors are thankful to an anonymous referee for his valuable suggestions which have led to substantial improvement in the presentation of this manuscript. Authors also extend their sincere thanks to the Editor and an Associate Editor for useful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.