Estimating the Entropy of a Weibull Distribution under Generalized Progressive Hybrid Censoring

Abstract

Recently, progressive hybrid censoring schemes have become quite popular in a life-testing problem and reliability analysis. However, the limitation of the progressive hybrid censoring scheme is that it cannot be applied when few failures occur before time T . Therefore, a generalized progressive hybrid censoring scheme was introduced. In this paper, the estimation of the entropy of a two-parameter Weibull distribution based on the generalized progressively censored sample has been considered. The Bayes estimators for the entropy of the Weibull distribution based on the symmetric and asymmetric loss functions, such as the squared error, linex and general entropy loss functions, are provided. The Bayes estimators cannot be obtained explicitly, and Lindley's approximation is used to obtain the Bayes estimators. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, a real dataset has been analyzed for illustrative purposes.

Parameters Estimation for the Exponentiated Weibull Distribution Based on Generalized Progressive Hybrid Censoring Schemes

“…This censoring scheme proposed by Cho et al [3] and can be described as follows: Consider a life-testing experiment in which n identical units are put to testing. Assume that ( ) ( ) ( ) Figure 1.…”

“…Some recent studies on Type-I and Type-II GPHCSs have been carried out by many authors, including, Cho et al [3] considered the Bayesian and maximum likelihood estimations for the entropy of Weibull distribution based on Type-I GPHCS. Cho et al [4] obtained the exact distribution of the MLE as well as exact lower confidence bound for the exponential parameter under Type-I GPHCS.…”

“…One limitation of the Type-I PHCS, that is cannot be applied it when very few failures may occur before time T accordingly the MLE for a parameter of underling lifetime model of observations may not be computed or its accuracy will be extremely low. Therefore, Cho et al [3] suggested this Type of censoring to allow the experiment to continue beyond time T and observed a pre-specified number of failures if very few failures had been observed up to time .…”

“…Type-I and Type-II generalized progressive hybrid censoring schemes (GPHCSs) proposed to overcome the drawbacks of the Type-I PHCS and Type-II PHCS, respectively. Cho et al [3] proposed a new censoring scheme called GPHCS to overcome the drawback of the Type-I PHCS. One limitation of the Type-I PHCS, that is cannot be applied it when very few failures may occur before time T accordingly the MLE for a parameter of underling lifetime model of observations may not be computed or its accuracy will be extremely low.…”

Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample

“…Yang [5] derived the maximum likelihood estimation of Weibull distribution under Type II progressive censoring with random removals, where the number of units removed at each failure time follows a binomial distribution.Wu [6] considered the estimation problem of the two-parameter bathtub-shaped lifetime distribution based a progressively type-II censored sample. Cho et al [7] discussed the Bayes estimation of the entropy of a twoparameter Weibull distribution based on the generalized progressively censored sample. Bhattacharya et al [8] proposed an optimum life-testing plans under Type-II progressive censoring scheme using variable neighborhood search algorithm.…”