E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications

Hassan M. Okasha, Heba S. Mohammed and Yuhlong Lio
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Hassan M. Okasha: Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Heba S. Mohammed: Mathematical Sciences Department, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11671, Saudi Arabia
Yuhlong Lio: Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA

Mathematics, 2021, vol. 9, issue 11, 1-19

Abstract: Given a progressively type-II censored sample, the E-Bayesian estimates, which are the expected Bayesian estimates over the joint prior distributions of the hyper-parameters in the gamma prior distribution of the unknown Weibull rate parameter, are developed for any given function of unknown rate parameter under the square error loss function. In order to study the impact from the selection of hyper-parameters for the prior, three different joint priors of the hyper-parameters are utilized to establish the theoretical properties of the E-Bayesian estimators for four functions of the rate parameter, which include an identity function (that is, a rate parameter) as well as survival, hazard rate and quantile functions. A simulation study is also conducted to compare the three E-Bayesian and a Bayesian estimate as well as the maximum likelihood estimate for each of the four functions considered. Moreover, two real data sets from a medical study and industry life test, respectively, are used for illustration. Finally, concluding remarks are addressed.

Keywords: E-Bayes estimation; Bayes estimation; a two-parameter Weibull distribution; progressive type-II censoring; square loss function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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