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Bayesian and maximum likelihood estimations from exponentiated log-logistic distribution based on progressive type-II censoring under balanced loss functions
Communications for Statistical Applications and Methods 2021;28:425-445
Published online September 30, 2021
© 2021 Korean Statistical Society.

Younshik Chunga, Yeongju Oh1,b

aDepartment of Statistics, Pusan National University, Busan, Korea;
bStatistical Methodology Division, Statistics Research Institute, Daejeon, Korea
Correspondence to: 1 Statistical Methodology Division, Statistics Research Institute, 713, Hanbat-daero, Seo-gu, Daejeon, Republic of Korea. E-mail: oyj1928@korea.kr
Received January 22, 2021; Revised June 18, 2021; Accepted June 18, 2021.
 Abstract
A generalization of the log-logistic (LL) distribution called exponentiated log-logistic (ELL) distribution on lines of exponentiated Weibull distribution is considered. In this paper, based on progressive type-II censored samples, we have derived the maximum likelihood estimators and Bayes estimators for three parameters, the survival function and hazard function of the ELL distribution. Then, under the balanced squared error loss (BSEL) and the balanced linex loss (BLEL) functions, their corresponding Bayes estimators are obtained using Lindley’s approximation (see Jung and Chung, 2018; Lindley, 1980), Tierney-Kadane approximation (see Tierney and Kadane, 1986) and Markov Chain Monte Carlo methods (see Hastings, 1970; Gelfand and Smith, 1990). Here, to check the convergence of MCMC chains, the Gelman and Rubin diagnostic (see Gelman and Rubin, 1992; Brooks and Gelman, 1997) was used. On the basis of their risks, the performances of their Bayes estimators are compared with maximum likelihood estimators in the simulation studies. In this paper, research supports the conclusion that ELL distribution is an ecient distribution to modeling data in the analysis of survival data. On top of that, Bayes estimators under various loss functions are useful for many estimation problems.
Keywords : balanced loss functions, Lindley’s approximation, Tierney-Kadane approximation, Markov Chain Monte Carlo (MCMC) method, exponentiated log-logistic distribution, progressive type-II censoring