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Probability matching priors for the powers of mean and variance in the normal distribution
Journal of the Korean Data & Information Science Society 2018;29:827-37
Published online May 31, 2018
© 2018 Korean Data and Information Science Society.

Jeong Hwan Ko1 · Sang Gil Kang2 · Woo Dong Lee3

1Department of Information Statistics, Andong National University
2Department of Computer and Data Information, Sangji University
3Pre-major of Cosmetics and Pharmaceutics, Daegu Haany University
Correspondence to: Professor, Department of Computer and Data Information, Sangji University, Wonju 26339, Korea. E-mail:
Received March 30, 2018; Revised April 27, 2018; Accepted April 30, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper considers the noninformative priors for the powers of mean and variance in the normal distribution. The powers of mean and variance include the inverse powers of mean, the coefficient of variation and the inverse of the coefficient of variation, etc. We develop probability matching priors as the noninformative priors. Then we reveal that Jeffreys' prior and the developed matching prior have the different density forms. Based on the general priors including the derived noninformative priors, we investigate the condition that the posterior distributions are proper. We show that the the first order matching prior corresponds very well the frequentist target coverage probabilities than Jeffreys' prior through simulation study, and a real example is illustrated.
Keywords : Matching prior, normal distribution, powers of mean and variance.