Estimation in Weibull Distribution Under Progressively Type-I Hybrid Censored Data

Abstract

In this article, we consider the estimation of unknown parameters of Weibull distribution when the lifetime data are observed in the presence of progressively type–I hybrid censoring scheme. The Newton–Raphson algorithm, Expectation–Maximization (EM) algorithm and Stochastic EM algorithm are utilized to derive the maximum likelihood estimates for the unknown parameters. Moreover, Bayesian estimators using Tierney–Kadane Method and Markov Chain Monte Carlo method are obtained under three different loss functions, namely, squared error loss, linear–exponential and generalized entropy loss functions. Also, the shrinkage pre–test estimators are derived. An extensive Monte Carlo simulation experiment is conducted under different schemes so that the performances of the listed estimators are compared using mean squared error, confidence interval length and coverage probabilities. Asymptotic normality and MCMC samples are used to obtain the confidence intervals and highest posterior density intervals respectively. Further, a real data example is presented to illustrate the methods. Finally, some conclusive remarks are presented.

Keywords

• Bayesian estimation
• EM algorithm
• SEM algorithm
• Tierney-Kadane’s approximation
• progressively type-I hybrid censoring
• Weibull distribution