• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.425-445
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• 2021

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 efficient 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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.441-451
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• 2013

In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.