• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.53-66
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• 1993

A Bayesian approach is suggested to the multi-proportions randomized response model. O'Hagan's (1987) Bayes linear estimator is extended to the inference of unrelated question-type randomized response model. Also some numerical comparisons are provided to show the performance of the Bayes linear estimator under the Dirichlet prior.

• Journal of the Korean Statistical Society
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• v.27 no.1
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• pp.1-10
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• 1998

In the problem of estimating a vector of unknown regression coefficients under the sum of squared error losses in a hierarchical linear model, we propose the hierarchical Bayes estimator of a vector of unknown regression coefficients in a hierarchical linear model, and then prove the admissibility of this estimator using Blyth's (196\51) method.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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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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• v.15 no.2
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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.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.221-235
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• 1999

Let be $X_1$,...,$X_p$, $p\geq2$ independent random variables where each $X_i$ has a gamma distribution with $\textit{k}_i$ and $\theta_i$ The problem is to simultaneously estimate $\textit{p}$ gamma parameters $\theta_i$ and $\theta_i{^-1}$ under entropy loss where the parameters are believed priori. Hierarch ical Bayes(HB) and empirical Bayes(EB) estimators are investigated. And a preference of HB estimator over EB estimator is shown using Gibbs sampler(Gelfand and Smith 1990). Finally computer simulation is studied to compute the risk percentage improvements of the HB estimator and the estimator of Dey Ghosh and Srinivasan(1987) compared to UMVUE estimator of $\theta^{-1}$.

• Communications for Statistical Applications and Methods
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• v.25 no.4
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• pp.355-371
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• 2018

The two parameter negative exponential distribution has many practical applications in queuing theory such as the service times of agents in system, the time it takes before your next telephone call, the time until a radioactive practical decays, the distance between mutations on a DNA strand, and the extreme values of annual snowfall or rainfall; consequently, has many applications in reliability systems. This paper considers an estimation problem of stress-strength model with two parameter negative parameter exponential distribution. We introduce a maximum penalized likelihood method, Bayes estimator using Lindley approximation to estimate stress-strength model and compare the proposed estimators with regular maximum likelihood estimator for complete data. We also introduce a maximum penalized likelihood method, Bayes estimator using a Markov chain Mote Carlo technique for incomplete data. A Monte Carlo simulation study is performed to compare stress-strength model estimates. Real data is used as a practical application of the proposed model.

• Journal of Korean Society for Quality Management
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• v.43 no.1
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• pp.57-66
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• 2015

Purpose: The purpose of this study is to apply the constrained Bayesian estimation methodology for product quality control process and prove the effectiveness of the product management by comparing with the well-known Bayes estimator through data performance result. Methods: The Bayes and constrained Bayes estimators were produced based on the theoretical background and for confirming the effectiveness of suggested application, the deviation index was defined and calculated for the comparison. Results: The statistical analysis result shows that applying the suggested estimation methodology, that is, constrained Bayes estimator improves the effectiveness of the index with regard to reduce the error by matching the first two empirical moments. Conclusion: Considering the advanced Bayesian approaches such as constrained Bayes estimation for the product quality control process, the newly defined deviation index reduces the error for estimating the parameter histogram which is reflected both location and deviation parameters and furthermore various Bayesian perspective approaches seems to be meaningful for managing the product quality control process.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1251-1256
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• 2011

Consider a p-variate ($p{\geq}4$) normal distribution with mean ${\theta}$ and identity covariance matrix. Using a simple property of noncentral chi square distribution, the generalized Bayes estimators dominating the Lindley estimator under quadratic loss are given based on the methods of Brown, Brewster and Zidek for estimating a normal variance. This result can be extended the cases where covariance matrix is completely unknown or ${\Sigma}={\sigma}^2I$ for an unknown scalar ${\sigma}^2$.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.261-274
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• 2014

In this paper we develop Bayes and empirical Bayes estimators of the finite population mean with the assumption of posterior linearity rather than normality of the superpopulation under the balanced loss function. We compare the performance of the optimal Bayes estimator with ones of the classical sample mean and the usual Bayes estimator under the squared error loss with respect to the posterior expected losses, risks and Bayes risks when the underlying distribution is normal as well as when they are binomial and Poisson.

• Journal of Korean Society for Quality Management
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• v.25 no.3
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• pp.108-118
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• 1997

A commercial nuclear power station contains at least two emergency diesel generates(EDG) to control the risk of severe core demage during the station blackout accidents. Therefore the reliability of the EDG's to start and load-run on demend must be maintained at a sufficiently high level. Until now, a simple assessment of start and load-run success rates was used to calculate the EDG's reliability. However, this method has been found to contain many defects. Recently, the work of Martz et al.(1996) proposed the use of the Bayes estimator to find the EDG's reliability. In this paper, we will propose confidence interval for the Bayes estimator, compare the above two methods and, using practical examples, illustrate why the Bayes estimator method is more reasonable in our situation.