• The Korean Journal of Applied Statistics
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• v.26 no.5
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• pp.713-723
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• 2013

An objective Bayesian estimation procedure of the two-parameter Pareto distribution is presented under the reference prior and the noninformative prior. Bayesian estimators are obtained by Gibbs sampling. The steps to generate parameters in the Gibbs sampler are from the shape parameter of the gamma distribution and then the scale parameter by the adaptive rejection sampling algorism. A numerical study shows that the proposed objective Bayesian estimation outperforms other estimations in simulated bias and mean squared error.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.689-699
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• 2013

This paper studies the partial credibility application method by assuming the empirical prior or noninformative prior informations in auto insurnace business where intensive rating segmentation is expanded because of premium competition. Expanding of rating factor segmetation brings the increase of pricing cells, as a result, the number of cells for partial credibility application will increase correspondingly. This study is trying to suggest more accurate estimation method by considering the Bayesian framework. By using empirically well-known or noninformative information, inducing the proper posterior distribution and applying the Bayes estimate which is minimizing the error loss into the credibility method, we will show the advantage of Bayesian inference by comparison with current approaches. The comparison is implemented with square root rule which is a widely accepted method in insurance business. The convergence level towarding to the true risk will be compared among various approaches. This study introduces the alternative way of redcuing the error to the auto insurance business fields in need of various methods because of more segmentations.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.255-266
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• 2007

A Bayesian estimation of the four-parameter gamma distribution is considered under the noninformative prior. The Bayesian estimators are obtained by the Gibbs sampling. The generation of the shape/power parameter and the power parameter in the Gibbs sampler is implemented using the adaptive rejection sampling algorithm of Gilks and Wild (1992). Also, the location parameter is generated using the adaptive rejection Metropolis sampling algorithm of Gilks, Best and Tan (1995). Finally, the simulation result is presented.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.201-207
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• 2002

In this paper, Jeffrey's and reference priors are derived when the parameter of interest is the ratio of means of two in dependent Poisson distribution. To achieve the parameter orthogonality in the sense of Cox and Reid (1987), non-trivial orthogonal transformation is provided. The orthogonal transformation makes to find noninformative priors easy. Our simulation study indicates that the reference prior meet very well the target coverage probabilities in a frequentist sense. Using the real data, we compute Bayes estimator and MLE for the ratio of means based on the reference prior.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.147-152
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• 2000

A Bayesian criterion is proposed for a multiple test of two independent multivariate normal populations. For a Bayesian test the fractional Bayes facto.(FBF) of O'Hagan(1995) is used under the assumption of Jeffreys priors, noninformative improper proirs. In this test the FBF without the need of sampling minimal training samples is much simpler to use than the intrinsic Bayes facotr(IBF) of Berger and Pericchi(1996). Finally, a simulation study is performed to show the behaviors of the FBF.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.355-363
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• 2007

In this paper a Bayesian estimation of the two-parameter kappa distribution was discussed under the noninformative prior. The Bayesian estimators are obtained by the Gibbs sampling. The generation of the shape parameter and scale parameter in the Gibbs sampler is implemented using the adaptive rejection Metropolis sampling algorithm of Gilks et al. (1995). A Monte Carlo study showed that the Bayesian estimators proposed outperform other estimators in the sense of mean squared error.

• Journal of the Korean Statistical Society
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• v.29 no.4
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• pp.443-454
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• 2000

In Bayesian model selection or testing problems of different dimensions, the conventional Bayes factors with improper noninformative priors are not well defined. The intrinsic Bayes factor and the fractional Bayes factor are used to overcome such problems by using a data-splitting idea and fraction, respectively. This article addresses a Bayesian testing for the comparison of two normal means with unknown variance. We derive proper intrinsic priors, whose Bayes factors are asymptotically equivalent to the corresponding fractional Bayes factor. We demonstrate our results with two examples.

• Journal of the Korean Data and Information Science Society
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• v.22 no.5
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• pp.1007-1016
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• 2011

This article deals with the problem of testing for the correlation coefficient in the bivariate normal distribution. We propose Bayesian hypothesis testing procedures for the bivariate normal correlation coefficient under the noninformative prior. The noninformative priors are usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. A simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.465-472
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• 2014

This article deals with the problem of testing the equality of the scale parameters in the half logistic distributions. We propose Bayesian hypothesis testing procedures for the equality of the scale parameters under the noninformative priors. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be dened up to a multiplicative constant. Thus we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.949-957
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• 2013

In this paper, we consider the problem of testing the equality of the scale parameters in two parameter exponential distributions. We propose Bayesian testing procedures for the equality of the scale parameters under the noninformative priors. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Thus, we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.