Non-informative priors in the generalized gamma stress–strength systems

Abstract

This article deals with non-informative priors for parameters when both stress and strength follow generalized gamma distributions. First, the orthogonal reparameterization is treated and then, using this reparameterization, Jeffreys’ prior, group ordering reference priors, and matching priors are derived. The propriety of posterior distributions is investigated and marginal posterior distributions are provided under those non-informative priors. The question of whether or not the reference priors satisfy the probability matching criterion is addressed. Finally, the reference prior that satisfies the probability matching criterion is shown to be good in the sense of frequentist coverage probability of the posterior quantile.

Accepted in 2005 for a special issue on Reliability co-edited by Hoang Pham, Rutgers University; Dong Ho Park, Hallym University, Korea; and Richard Cassady, University of Arkansas.

Keywords:

• Frequentist coverage probability
• generalized gamma distribution
• Jeffreys’ prior
• matching prior
• orthogonal reparametrization
• posterior
• reference prior
• system reliability

Acknowledgement

This work was supported by research funds from Chosun University, 2008.