Bayesian estimation for Rayleigh models
Ji Eun Oh1 · Joon Jin Song2 · Joong Kweon Sohn3
13Department of Statistics, Kyungpook National University
2Department of Statistical Science, Baylor University
2Department of Statistical Science, Baylor University
Correspondence to: Joong Kweon Sohn
Professor, Department of Statistics, Kyungpook National University, 80 Daehak-ro, Buk-gu, Daegu 41566, Korea, E-mail: jsohn@knu.ac.kr
Professor, Department of Statistics, Kyungpook National University, 80 Daehak-ro, Buk-gu, Daegu 41566, Korea, E-mail: jsohn@knu.ac.kr
Received April 27, 2017; Revised May 30, 2017; Accepted June 1, 2017.
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
- The Rayleigh distribution has been commonly used in life time testing studies of the probability of surviving until mission time. We focus on a reliability function of the Rayleigh distribution and deal with prior distribution on R(t). This paper is an effort to obtain Bayes estimators of rayleigh distribution with three different prior distribution on the reliability function; a noninformative prior, uniform prior and inverse gamma prior. We have found the Bayes estimator and predictive density function of a future observation y with each prior distribution. We compare the performance of the Bayes estimators under different sample size and in simulation study. We also derive the most plausible region, prediction intervals for a future observation.
- Keywords : Bayes estimator, inversed gamma prior, predictive distribution, predict in- tervals
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