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Bayesian estimation of P(Y < X) for Lévy distribution
Journal of the Korean Data & Information Science Society 2021;32:257-66
Published online January 31, 2021;  https://doi.org/10.7465/jkdi.2021.32.1.257
© 2021 Korean Data and Information Science Society.

Sang Gil Kang1

1Department of Computer and Data Information, Sangji University
Correspondence to: 1Professor, Department of Computer and Data Information, Sangji University, Wonju 26339, Korea. E-mail: sangkg@sangji.ac.kr

This research was supported by Sangji University Research Fund, 2019.
Received December 1, 2020; Revised December 24, 2020; Accepted December 26, 2020.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, we develop the noninformative priors for P(Y < X) when X and Y have independent Lévy distributions. We develop the matching priors and the reference pri- ors as the noninformative priors. The developed matching prior is a prior distribution that matches the alternatives coverage probabilities, and a prior distribution that sat- is es the criterion of a highest posterior density. In addition, we derived the reference prior, and it was shown that this reference prior becomes the second order matching prior, and is equal to Jeffreys' prior. Through simulations, we showed that the match- ing prior performs very reasonably in terms of coverage probability. Furthermore, the matching prior showed that even when the sample size was small, it was well matched with the target coverage probability. An example is given at the end.
Keywords : Matching prior, ratio of scale parameters, reference prior, stress-strength reliability.