• 품질경영학회지
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• 제13권1호
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• pp.2-11
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• 1985

We study some Bayes esimators of the reliability of k out of m stress-strength model under quadratic loss and various prior distributions. We obtain Bayes estimators, Bayes risk, predictive bounds and asymtotic distribution of Bayes estimator. We investigate behaviours of Bayes estimator in moderate samples.

• Communications for Statistical Applications and Methods
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• 제6권2호
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• pp.501-510
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• 1999

In this paper, we consider a comparable study on three Bayes procedures for the multivariate normal mean estimation problem. In specific we consider hierarchical Bayes empirical Bayes and robust Bayes estimators for the normal means. Then three procedures are compared in terms of the four comparison criteria(i.e. Average Relative Bias (ARB) Average Squared Relative Bias (ASRB) Average Absolute Bias(AAB) Average Squared Deviation (ASD) using the real data set.

• Journal of the Korean Statistical Society
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• 제35권3호
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• pp.317-329
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• 2006

In the problem of estimating the error variance in the balanced fixed- effects one-way analysis of variance (ANOVA) model, Ghosh (1994) proposed hierarchical Bayes estimators and raised a conjecture for which all of his hierarchical Bayes estimators are admissible. In this paper we prove this conjecture is true by representing one-way ANOVA model to the distributional form of a multiparameter exponential family.

• 품질경영학회지
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• 제15권1호
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• pp.20-32
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• 1987

Estimation for the parameters of a bivariate exponential (BVE) model of Marshall and Olkin (1967) is investigated for the cases of complete sampling and time-truncated parallel sampling. Maximum likelihood estimators, method of moment estimators and Bayes estimators for the parameters of a BVE model are obtained and compared with each other. A Monte Cario simulation study for a moderate sized samples indicates that the Bayes estimators of parameters perform better than their maximum likelihood and method of moment estimators.

• Communications for Statistical Applications and Methods
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• 제28권5호
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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 Korean Data and Information Science Society
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• 제28권3호
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• pp.659-668
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• 2017

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.

• Communications for Statistical Applications and Methods
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• 제11권3호
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• pp.619-629
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• 2004

Binomial group testing or composite sampling is often used to estimate the proportion, p, of positive(infects, defectives) in a population when that proportion is known to be small; the potential benefits of group testing over one-at-a-time testing are well documented. The literature has focused on maximum likelihood estimation. We provide two Bayes estimators and compare them with the MLE. The first of our Bayes estimators uses an uninformative Uniform (0, 1) prior on p; the properties of this estimator are poor. Our second Bayes estimator uses a much more informative prior that recognizes and takes into account key aspects of the group testing context. This estimator compares very favorably with the MSE, having substantially lower mean squared errors in all of the wide range of cases we considered. The priors uses a Beta distribution, Beta ($\alpha$, $\beta$), and some advice is provided for choosing the parameter a and $\beta$ for that distribution.

• Journal of the Korean Statistical Society
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• 제15권2호
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• pp.97-106
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• 1986

Assume that $X_1, X_2, \cdots, X_N$ are iid p-dimensional normal random vectors ($p \geq 3$) with unknown covariance matrix. The problem of estimating multivariate normal mean vector in an empirical Bayes situation is considered. Empirical Bayes estimators, obtained by Bayes treatmetn of the covariance matrix, are presented. It is shown that the estimators are minimax, each of which domainates teh maximum likelihood estimator (MLE), when the loss is nonsingular quadratic loss. We also derive approximate credibility region for the mean vector that takes advantage of the fact that the MLE is not the best estimator.

• Journal of the Korean Data and Information Science Society
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• 제17권3호
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• pp.1009-1019
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• 2006

In this paper, we consider the simultaneous estimation problem for the normal means. We set up the model structure using the several different distributions of the errors for observing their effects of model perturbation for the error terms in obtaining the empirical Bayes and hierarchical Bayes estimators. We compare the performance of those estimators under model perturbation based on a simulation study.

• Communications for Statistical Applications and Methods
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• 제20권4호
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• pp.321-327
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• 2013

Bayesian and empirical Bayesian methods have become quite popular in the theory and practice of statistics. However, the objective is to often produce an ensemble of parameter estimates as well as to produce the histogram of the estimates. For example, in insurance pricing, the accurate point estimates of risk for each group is necessary and also proper dispersion estimation should be considered. Well-known Bayes estimates (which is the posterior means under quadratic loss) are underdispersed as an estimate of the histogram of parameters. The adjustment of Bayes estimates to correct this problem is known as constrained Bayes estimators, which are matching the first two empirical moments. In this paper, we propose a way to apply the constrained Bayes estimators in insurance pricing, which is required to estimate accurately both location and dispersion. Also, the benefit of the constrained Bayes estimates will be discussed by analyzing real insurance accident data.