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.
Highlights
Entropy, which is one of the important terms in statistical mechanics, was originally defined in physics especially in the second law of thermodynamics
Cho et al [7] derived estimators for the entropy function of a Rayleigh distribution based on doubly-generalized Type II hybrid censored samples by using the maximum likelihood estimator (MLE), approximate MLEs and Bayes estimators
Kundu and Joarder [11] proposed a progressive hybrid censoring scheme in the context of a life-testing experiment in which n identical units are placed in an experiment with the progressive Type II censoring scheme (R1, R2, · · ·, Rm ), and the experiment is terminated at time min{Xm:m:n, T }, where T ∈ (0, ∞) and 1 ≤ m ≤ n are fixed in advance and X1:m:n ≤ X2:m:n ≤ · · · ≤ Xm:m:n are the ordered failure times from the experiment
Summary
Entropy, which is one of the important terms in statistical mechanics, was originally defined in physics especially in the second law of thermodynamics. Cho et al [7] derived estimators for the entropy function of a Rayleigh distribution based on doubly-generalized Type II hybrid censored samples by using the maximum likelihood estimator (MLE), approximate MLEs and Bayes estimators. This process continues, until, immediately following the m-th observed failure, all of the remaining Rm = n−R1 −· · ·−Rm−1 −m units are removed from the experiment In this experiment, the progressive censoring scheme R = (R1 , R2 , · · · , Rm ) is pre-fixed. MLE for a parameter of a underling distribution of observations may not be computed or its accuracy will be extremely low For this reason, Cho et al [7] propose a generalized progressive hybrid censoring scheme, which allows us to observe a pre-specified number of failures.
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