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Estimation of entropy of the inverse weibull distribution under generalized progressive hybrid censored data
Journal of the Korean Data & Information Science Society 2017;28:659-68
Published online May 31, 2017
© 2017 Korean Data & Information Science Society.

Kyeongjun Lee1

1Department of Computer Science and Statistics, Daegu University
Correspondence to: Kyeongjun Lee
Assistant professor, Department of Computer Science and Statistics, Daegu University, Gyeongsan 38453, Korea. E-mail: leekj@daegu.ac.kr
Received March 3, 2017; Revised April 12, 2017; Accepted April 19, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.
Keywords : Generalized progressive hybrid censoring, inverse weibull distribution, maximum likelihood estimation, Tierney and Kadane approximation.


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