• Communications for Statistical Applications and Methods
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• 제28권4호
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• pp.315-327
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• 2021

The Spatial Autoregressive (SAR) models have drawn considerable attention in recent econometrics literature because of their capability to model the spatial spill overs in a feasible way. While considering the Bayesian analysis of these models, one may face the problem of lack of robustness with respect to underlying prior assumptions. The generalized Bayes estimators provide a viable alternative to incorporate prior belief and are more robust with respect to underlying prior assumptions. The present paper considers the SAR model with a set of linear restrictions binding the regression coefficients and derives restricted generalized Bayes estimator for the coefficients vector. The minimaxity of the restricted generalized Bayes estimator has been established. Using a simulation study, it has been demonstrated that the estimator dominates the restricted least squares as well as restricted Stein rule estimators.

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.435-442
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• 2001

Bayes estimators and generalized ML estimators for reliability of a k-unit hot standby system with the perfect switch based upon a complete sample of failure times observed from an exponential distribution using noninformative, generalized uniform, and gamma priors for the failure rate are proposed, and MSE's of proposed several estimators for the standby system reliability are compared numerically each other through the Monte Carlo simulation.

• Journal of the Korean Statistical Society
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• 제27권4호
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• pp.385-396
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• 1998

A computing method of fractional Bayes factor (FBF) for a point null hypothesis is explained. We propose alternative form of FBF that is the product of density ratio and a quantity using the generalized Savage-Dickey density ratio method. When it is difficult to compute the alternative form of FBF analytically, each term of the proposed form can be estimated by MCMC method. Finally, two examples are given.

• Communications for Statistical Applications and Methods
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• 제27권4호
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• pp.413-430
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• 2020

The multiply Type-II hybrid censoring scheme is disadvantaged by an experiment time that is too long. To overcome this limitation, we propose a generalized multiply Type-II hybrid censoring scheme. Some estimators of the scale parameter of the exponential distribution are derived under a generalized multiply Type-II hybrid censoring scheme. First, the maximum likelihood estimator of the scale parameter of the exponential distribution is obtained under the proposed censoring scheme. Second, we obtain the Bayes estimators under different loss functions with a noninformative prior and an informative prior. We approximate the Bayes estimators by Lindleys approximation and the Tierney-Kadane method since the posterior distributions obtained by the two priors are complicated. In addition, the Bayes estimators are obtained by using the Markov Chain Monte Carlo samples. Finally, all proposed estimators are compared in the sense of the mean squared error through the Monte Carlo simulation and applied to real data.

• 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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• 제3권3호
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• pp.215-223
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• 1996

By using Tukey's generalized lambda distribution, appoximate posterior density is derived under the Bayes-empirical Bayes model. The sensitivity of posterior distribution to the hyperprior distribution is examined by using Tukey's generalized lambda distriburion which approximate many well-knmown distributions. Based upon Monte Varlo simulation studies it can be said that posterior distribution is sensitive to the cariance of the prior distribution and to the symmetry of the hyperprior distribution. Also posterior distribution is approximately obtained by using the following methods : Lindley method, Laplace method and Gibbs sampler method.

• Journal of the Korean Data and Information Science Society
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• 제28권1호
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• pp.217-225
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• 2017

This article deals with the problem of multiple hypothesis testing for the shape parameter in the generalized exponential distribution. We propose Bayesian hypothesis testing procedures for multiple hypotheses of the shape parameter with the noninformative prior. The Bayes factor with the noninformative prior is not well defined. The reason is that the most of the noninformative prior can be improper. Therefore we study the default Bayesian multiple hypothesis testing methods using the fractional and intrinsic Bayes factors with the reference priors. Simulation study is performed and an example is given.

• Communications for Statistical Applications and Methods
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• 제20권1호
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• pp.29-39
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• 2013

This paper derives maximum likelihood estimators (MLEs) and some approximate MLEs (AMLEs) of unknown parameters of the generalized exponential distribution when data are lower record values. We derive approximate Bayes estimators through importance sampling and obtain corresponding Bayes predictive intervals for unknown parameters for lower record values from the generalized exponential distribution. For illustrative purposes, we examine the validity of the proposed estimation method by using real and simulated data.

• Journal of the Korean Data and Information Science Society
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• 제13권2호
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• pp.227-234
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• 2002

In this paper, we consider hierarchical Bayes generalized linear models for the analysis of longitudinal count data. Specifically we introduce the hierarchical Bayes random effects models. We discuss implementation of the Bayes procedures via Markov chain Monte Carlo (MCMC) integration techniques. The hierarchical Baye method is illustrated with a real dataset and is compared with other statistical methods.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.141-150
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• 2000

In this paper we propose a method of computing Bayes factor to detect an outlier in a random effects model. When no information is available and hence improper noninformative priors should be used Bayes factor includes the unspecified constants and has complicated computational burden. To solve this problem we use the fractional Bayes factor (FBF) of O-Hagan(1995) and the generalized Savage0-Dickey density ratio of Verdinelli and Wasserman (1995) The proposed method is applied to outlier deterction problem We perform a simulation of the proposed approach with a simulated data set including an outlier and also analyze a real data set.