• Communications for Statistical Applications and Methods
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• 제20권5호
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• pp.387-394
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• 2013

In this paper, we develop the noninformative priors for the ratio of the scale parameters in the inverted exponential distributions. The first and second order matching priors, the reference prior and Jeffreys prior are developed. It turns out that the second order matching prior matches the alternative coverage probabilities, is a cumulative distribution function matching prior and is a highest posterior density matching prior. In addition, the reference prior and Jeffreys' prior are the second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study as well as provide an example based on real data is given.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2005년도 추계학술대회
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• pp.71-84
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• 2005

The Fieller-Creasy problem involves statistical inference about the ratio of two independent normal means. It is difficult problem from either a frequentist or a likelihood perspective. As an alternatives, a Bayesian analysis with noninformative priors may provide a solution to this problem. In this paper, we extend the results of Yin and Ghosh (2001) to unbalanced sample case. We find various noninformative priors such as first and second order matching priors, reference and Jeffreys' priors. The posterior propriety under the proposed noninformative priors will be given. Using real data, we provide illustrative examples. Through simulation study, we compute the frequentist coverage probabilities for probability matching and reference priors. Some simulation results will be given.

• 응용통계연구
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• 제17권1호
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• pp.49-60
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• 2004

이 논문의 목적은 역 가우스 분포의 모수비가 관심의 대상일 때, 그 모수비에 대한 무정보적 사전분포를 구하는데 있다. 특별히, 모수비에 대한 확률대응사전분포와 기준 사전분포를 제안하였다. 먼저, 관심의 대상이 되는 모수에 대해 모수 직교화 변환을 구하고, 모수 직교화 변환을 이용하여 확률대응사전분포와 기준사전분포를 구하였다. 특히 확률대응사전분포의 일치차수는 1차임을 보였으며 2차 확률대응사전분포는 존재하지 않음을 보였다. 또한 제안된 사전분포에 의해 유도된 사후분포는 적절 분포임을 증명하였다. 모의 실험을 통하여 확률대응사전분포와 기준사전분포를 비교했으며, 실제자료를 이용하여 분석하는 예를 보였다.

• Journal of the Korean Data and Information Science Society
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• 제27권2호
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• pp.565-575
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• 2016

In this paper, we develop the noninformative priors for the linear combinations of means in the exponential distributions. We develop the matching priors and the reference priors. The matching priors, the reference prior and Jeffreys' prior for the linear combinations of means are developed. It turns out that the reference prior and Jeffreys' prior are not a matching prior. We show that the proposed matching prior matches the target coverage probabilities much more accurately than the reference prior and Jeffreys' prior in a frequentist sense through simulation study, and an example based on real data is given.

• Communications for Statistical Applications and Methods
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• 제18권4호
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• pp.467-475
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• 2011

This paper develops the noninformative priors for the stress-strength reliability from one parameter generalized exponential distributions. When this reliability is a parameter of interest, we develop the first, second order matching priors, reference priors in its order of importance in parameters and Jeffreys' prior. We reveal that these probability matching priors are not the alternative coverage probability matching prior or a highest posterior density matching prior, a cumulative distribution function matching prior. In addition, we reveal that the one-at-a-time reference prior and Jeffreys' prior are actually a second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study and a provided example.

• Journal of the Korean Data and Information Science Society
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• 제13권2호
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• pp.235-242
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• 2002

In this paper, we develop noninformative priors that are used for estimating the ratio of failure rates under Freund's bivariate exponential distribution. A class of priors is found by matching the coverage probabilities of one-sided Baysian credible interval with the corresponding frequentist coverage probabilities. Also the propriety of posterior under the noninformative priors is proved and the frequentist coverage probabilities are investigated for small samples via simulation study.

• Journal of the Korean Statistical Society
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• 제32권3호
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• pp.271-288
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• 2003

In this paper, when the variance of the normal distribution is related to the mean, we develop noninformative priors such as matching priors and reference priors. We prove that the second order matching prior matches alternative coverage probabilities up to the same order and also it is a HPD matching prior. It turns out that one-at-a-time reference prior satisfies a second order matching criterion. Then using these noninformative priors, we develop a Bayesian test procedure for the equality of the means and variances of two independent normal distributions using fractional Bayes factor. Some simulation study is performed, and a real data example is also provided.

• Journal of the Korean Data and Information Science Society
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• 제25권1호
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• pp.227-235
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• 2014

In this paper, we develop the noninformative priors for the scale parameter and the shape parameter in the log-logistic distribution. We developed the first and second order matching priors. It turns out that the second order matching prior matches the alternative coverage probabilities, and is a highest posterior density matching prior. Also we revealed that the derived reference prior is the second order matching prior for both parameters, but Jerffrey's prior is not a second order matching prior. We showed that the proposed reference prior matches the target coverage probabilities in a frequentist sense through simulation study, and an example based on real data is given.

• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.763-772
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• 2015

In this paper, we develop the noninformative priors for the product of different powers of k means in the exponential distribution. We developed the first and second order matching priors. It turns out that the second order matching prior matches the alternative coverage probabilities, and is the highest posterior density matching prior. Also we revealed that the derived reference prior is the second order matching prior, and Jeffreys' prior and reference prior are the same. We showed that the proposed reference prior matches very well the target coverage probabilities in a frequentist sense through simulation study, and an example based on real data is given.

• Journal of the Korean Data and Information Science Society
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• 제23권4호
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• pp.833-841
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• 2012

In this paper, we develop the noninformative priors for the ratio of the scale parameters in the half logistic distributions. We develop the first and second order matching priors. It turns out that the second order matching prior matches the alternative coverage probabilities, and is a highest posterior density matching prior. Also we reveal that the one-at-a-time reference prior and Jeffreys' prior are the second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through simulation study, and an example based on real data is given.