• Journal of the Korean Data and Information Science Society
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• 제25권3호
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• pp.685-696
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• 2014

In this paper, we develop Bayesian inference of the finite population mean with the assumption of posterior linearity rather than normality of the superpopulation in the presence of auxiliary information under the balanced loss function. We compare the performance of the optimal Bayes estimator under the balanced loss function with ones of the classical ratio estimator and the usual Bayes estimator in terms of the posterior expected losses, risks and Bayes risks.

• 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.

• Communications for Statistical Applications and Methods
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• 제27권1호
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• pp.47-64
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• 2020

In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

• 품질경영학회지
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• 제23권3호
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• pp.113-125
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• 1995

This paper describes the 2-stage randomized response model in the Bayesian view point. The classical Bayesian analysis needs the complete information for a prior density, but the Bayes linear estimator needs only the first and second moments. Therefore, it is convenient to find the estimator and this estimator robusts to a prior density. We show that MSE's of the Bayes linear estimators for the 2-stage randomized response models are smaller than those of the MLE's for the 2-stage randomized response models.

• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.631-639
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• 2003

Bayes estimates of reliability for the stress-strength system are obtained with respect to LINEX loss function. A reference prior distribution of the reliability is derived and Bayes estimates of the reliability are also obtained. These Bayes estimates are compared with corresponding estimates under squared-error loss function.

• Communications for Statistical Applications and Methods
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• 제22권6호
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• pp.531-542
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• 2015

In this survey, we use the normal linear model to demonstrate the use of the linear Bayes method. The superiorities of linear Bayes estimator (LBE) over the classical UMVUE and MLE are established in terms of the mean squared error matrix (MSEM) criterion. Compared with the usual Bayes estimator (obtained by the MCMC method) the proposed LBE is simple and easy to use with numerical results presented to illustrate its performance. We also examine the applications of linear Bayes method to some other distributions including two-parameter exponential family, uniform distribution and inverse Gaussian distribution, and finally make some remarks.

• International Journal of Reliability and Applications
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• 제16권2호
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• pp.55-79
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• 2015

It is well known that using any additional information in the estimation of unknown parameters with new sample of observations diminishes the sampling units needed and minimizes the risk of new estimators. There are many rational reasons to assure that the existence of additional information in practice and there exists many practical cases in which additional information is available in the form of target value (initial value) about the unknown parameters. This article is described the problem of how the prior initial value about the unknown parameters can be utilized and combined with classical Bayes estimator to get a new combination of Bayes estimator and prior value to improve the properties of the new combination. In this article, two classes of Bayes-shrinkage and preliminary test Bayes-shrinkage estimators are proposed for the scale parameter of exponential distribution. The bias, risk and risk ratio expressions are derived and studied. The performance of the proposed classes of estimators is studied for different choices of constants engaged in the estimators. The comparisons, conclusions and recommendations are demonstrated.

• 품질경영학회지
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• 제13권2호
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• pp.8-12
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• 1985

We study the Bayes estimation procedure of ${\theta}=P_r$=(Y < X) when the experiment is terminated before all of the items on the test have failed and the failed items are partially replaced. Comparisons with the M.L.E., M.V.U.E. and Bayes estimator are made through Monte Carlo simulation.

• Journal of the Korean Statistical Society
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• 제12권1호
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• pp.1-9
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• 1983

A stress-strength model is formulated for s out of k system of identical components. We consider the estimation of system reliability from survival count data from a Bayesian viewpoint. We assume a quadratic loss and a Dirichlet prior distribution. It is shown that a Bayes sequential procedure can be established. The Bayes estimator is compared with the UMVUE obtained by Bhattacharyya and with an estimator based on Mann-Whitney statistic.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.545-556
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• 2005

Hjort(1990) obtained the nonparametric Bayes estimator $\^{F}_{c,a}$ of $F_0$ with respect to beta processes in the random censorship model. Let $X_1,{\cdots},X_n$ be i.i.d. $F_0$ and let $C_1,{\cdot},\;C_n$ be i.i.d. G. Assume that $F_0$ and G are continuous. This paper shows that {$\^{F}_{c,a}$(u){\|}0 < u < T} converges weakly to a Gaussian process whenever T < $\infty$ and $\~{F}_0({\tau})\;<\;1$.