• Communications for Statistical Applications and Methods
• /
• v.20 no.5
• /
• pp.387-394
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• v.18 no.4
• /
• pp.467-475
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• v.12 no.3
• /
• pp.729-742
• /
• 2005

In this paper, we discuss the propriety of the various noninformative priors for the Pareto distribution. The reference prior, Jeffreys prior and ad hoc noninformative prior which is used in several literatures will be introduced and showed that which prior gives the proper posterior distribution. The reference prior and Jeffreys prior give a proper posterior distribution, but ad hoc noninformative prior which is proportional to reciprocal of the parameters does not give a proper posterior. To compute survival function, we use the well-known approximation method proposed by Lindley (1980) and Tireney and Kadane (1986). And two methods are compared by simulation. A real data example is given to illustrate our methodology.

• Communications for Statistical Applications and Methods
• /
• v.9 no.2
• /
• pp.401-410
• /
• 2002

This paper revisits parallel-line bioassay problem, from a Bayesian point of view using noninformative priors such as Jeffreys' prior, reference priors, and probability matching priors. After finding the orthogonal transformation, the class of first order and second order probability matching priors are derived. Jeffreys' prior and reference priors are derived also. Numerical examples are given to show the effectiveness of noninformative priors.

• Communications for Statistical Applications and Methods
• /
• v.15 no.3
• /
• pp.429-440
• /
• 2008

In this paper, we develop the noninformative priors when the parameter of interest is the common coefficient of variation in two inverse Gaussian distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that the one-at-a-time and two group reference priors satisfy the first order matching criterion but Jeffreys' prior does not. The Bayesian credible intervals based on the one-at-a-time reference prior meet the frequentist target coverage probabilities much better than that of Jeffreys' prior. Some simulations are given.

• Journal of the Korean Statistical Society
• /
• v.29 no.1
• /
• pp.17-27
• /
• 2000

In this paper, we develop noninformative priors that are used for estimating the reliability of stress-strength system under the Burr-type X model. A class of priors is found by matching the coverage probabilities of one-sided Bayesian credible interval with the corresponding frequentist coverage probabilities. It turns out that the reference prior as well as the Jeffreys prior are the second order matching prior. The propriety of posterior under the noninformative priors is proved. The frequentist coverage probabilities are investigated for samll samples via simulation study.

• Communications for Statistical Applications and Methods
• /
• v.14 no.2
• /
• pp.431-442
• /
• 2007

In this paper, we develop the noninformative priors when the parameter of interest is the difference between quantiles of two exponential distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that Jeffreys' prior does not satisfy the first order matching criterion. The Bayesian credible intervals based on the first order probability matching prior meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior. Some simulation and real example will be given.

• The Korean Journal of Applied Statistics
• /
• v.15 no.2
• /
• pp.405-414
• /
• 2002

We consider the problem of estimating the error variance of in a two-way mixed-effects ANOVA model using noninformative priors. First, we derive Jeffreys' prior, a reference prior, and matching priors. We then provide marginal posterior distributions under those noninformative priors. Finally, we provide graphs of marginal posterior densities of the error variance and credible intervals for the error variance in two real data set and compare these credible intervals.

• 한국데이터정보과학회:학술대회논문집
• /
• 2005.04a
• /
• pp.135-144
• /
• 2005

In this paper, we develop the noninformative priors for the exponential models when the parameter of interest is the difference of two means. We develop the first and second order matching priors. We reveal that the second order matching priors do not exist. It turns out that Jeffreys' prior does not satisfy a first order matching criterion. The Bayesian credible intervals based on the first order matching meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior.

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.1
• /
• pp.83-92
• /
• 2003

In this paper, we derive noninformative priors for the ratio of parameters in the Burr model. We obtain Jeffreys' prior, reference prior and second order probability matching prior. Also we prove that the noninformative prior matches the alternative coverage probabilities and a HPD matching prior up to the second order, respectively. Finally, we provide simulated frequentist coverage probabilities under the derived noninformative priors for small and moderate size of samples.