Bayes and Maximum Likelihood Estimation of Uncertainty Measure of the Inverse Weibull Distribution under Generalized Adaptive Progressive Hybrid Censoring

Kyeongjun Lee ()
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Kyeongjun Lee: Department of Mathematics and Big Data Science, Kumoh National Institute of Technology, Gumi 39177, Gyeongbuk, Republic of Korea

Mathematics, 2022, vol. 10, issue 24, 1-20

Abstract: The inverse Weibull distribution (IWD) can be applied to a various situations, including applications in reliability and medicine. In a reliability and medicine test, it is generally known that the results of test units may not be recorded. Recently, the generalized adaptive progressive hybrid censoring (GAPHC) scheme was introduced. In this paper, therefore, we consider the classical estimators (maximum likelihood estimator (MLE) and maximum product spacings estimator (MPSE)) and Bayes estimators (BayEsts) of the uncertainty measure of the IWD under GAPHC scheme. We derive the BayEsts of the uncertainty measure based on flexible (symmetrical and asymmetrical) priors. Additionally, we derive the Bayes estimators using the Tierney and Kadane approximation (TiKa) and importance sampling methods. In particular, the importance sampling method is used to obtain the credible interval for the uncertainty measure of the IWD under the GAPHC scheme. To compare the proposed estimators (classical and BayEsts), the Monte Carlo simulation method is conducted. Finally, the real dataset based on GAPHC scheme is analyzed.

Keywords: Bayes estimator; generalized adaptive progressive hybrid censoring; inverse Weibull distribution; maximum likelihood estimator; maximum product spacings estimator; Tierney and Kadane approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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