Statistical inference for bathtub-shaped distribution based on generalized progressive hybrid censored data

Abstract

This paper is an effort to obtain the point estimators and interval estimators for the unknown parameters, reliability and hazard rate functions of bathtub-shaped distribution based on generalized progressive hybrid censoring. We first derive the maximum likelihood estimators for the quantities and compute the estimates using Newton iterative method. Observed Fisher’s information matrix is obtained and then the asymptotic confidence intervals are constructed. Besides, two bootstrap confidence intervals are proposed for the quantities. The Bayesian estimators are acquired under squared error loss function using Lindley method and Metropolis-Hastings method with Gibbs sampling, and Bayesian credible intervals are constructed based on Markov Chain Monte Carlo (MCMC) samples as well. Finally, extensive simulation studies are conducted to compare the performance of the estimators and a real data set is analyzed for illustrative purpose.