• Journal of the Korean Data and Information Science Society
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• 제9권2호
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• pp.211-218
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• 1998

This paper deals with the problem of obtaining some Bayes estimators of exponential reliability in a time censored sampling with incomplete information. Some Bayes estimators are proposed and studied under squared error loss and Harris loss.

• Journal of the Korean Statistical Society
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• 제19권1호
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• pp.88-92
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• 1990

In the problem of the recovery of interblock information in balanced incomplete block designs(BIBD), it is well known that a truncated estimator dominates the untruncated estimator under mean squared error loss. This paper shows that the domination result holds universally for every nondecreasing loss function.

• Journal of the Korean Data and Information Science Society
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• 제1권
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• pp.35-45
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• 1990

The problem of estimating the reliability using the Bayesian approach and the prior information about tile reliability of a lognormal distribution is considered. Some Bayes estimators are proposed and studied under the squared error loss and tile Harris loss. Also Monte Carlo simulations are carried out to examine the performances of the proposed estimators and results are provided in the tables.

• Communications for Statistical Applications and Methods
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• 제14권2호
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• pp.389-399
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• 2007

In this paper, Bayes estimates for the parameters k, c and reliability function of the Burr type XII model based on a type II censored samples under asymmetric loss functions viz., LINEX and SQUAREX loss functions are obtained. An approximation based on the Laplace approximation method (Tierney and Kadane, 1986) is used for obtaining the Bayes estimators of the parameters and reliability function. In order to compare the Bayes estimators under squared error loss, LINEX and SQUAREX loss functions respectively and the maximum likelihood estimator of the parameters and reliability function, Monte Carlo simulations are used.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.19-27
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• 2005

The present paper obtains Bayes estimators for the probability p(Y

• Communications for Statistical Applications and Methods
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• 제21권3호
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• pp.235-243
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• 2014

Constrained Bayesian estimates overcome the over shrinkness toward the mean which usual Bayes and empirical Bayes estimates produce by matching first and second empirical moments; subsequently, a constrained Bayes estimate is recommended to use in case the research objective is to produce a histogram of the estimates considering the location and dispersion. The well-known squared error loss function exclusively emphasizes the precision of estimation and may lead to biased estimators. Thus, the balanced loss function is suggested to reflect both goodness of fit and precision of estimation. In insurance pricing, the accurate location estimates of risk and also dispersion estimates of each risk group should be considered under proper loss function. In this paper, by applying these two ideas, the benefit of the constrained Bayes estimates and balanced loss function will be discussed; in addition, application effectiveness will be proved through an analysis of real insurance accident data.

• Communications for Statistical Applications and Methods
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• 제21권3호
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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 the Korean Statistical Society
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• 제31권4호
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• pp.415-431
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• 2002

A unified framework for statistical inference for the mean of the normal distribution to derive point estimates, confidence intervals and statistical tests is proposed. This optimal design is justified after investigating the basic information and requirements that are possible and impossible to control when specifying practical and statistical requirements. Point estimation is only credible when viewed in the larger context of interval estimation, since the information required for optimal point estimation is unspecifiable. Triple sampling is proposed and justified as a reasonable sampling vehicle to achieve the specifiable requirements within the unified framework.

• Communications for Statistical Applications and Methods
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• 제27권4호
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.219-234
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• 1993

A measuring instrument must be calibrated for accurate inferences of an unknown quantity. Bayesian calibration designs with respect to squared error loss based on a linear model are discussed in Kim and Barlow (1992). In this paper, we consider approximations of the optimal calibration designs using the idea of Gaussian inflence diagrams. The approximation is evaluated by means of numerical calculations, where it is compared with the exact values from the numerical integration.