On Estimation of Reliability for the Birnbaum-Saunders Fatigue Life Model.
SOUTH CAROLINA UNIV COLUMBIA DEPT OF MATHEMATICS AND STATISTICS
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The Birnbaum-Saunders fatigue life distribution with shape parameter alpha and scale parameter beta is considered. The scale parameter beta is also the median lifetime, and assuming that beta is known, Bayes estimators of the reliability function are obtained for a family of proper conjugate priors as well as for Jeffreys vague prior for alpha. When both alpha and beta are unknown, a modified Bayes estimator R sub Bt of the reliability is proposed using a moment estimator of beta. In addition to being computationally simpler than the maximum likelihood estimator mle of reliability, Monte Carlo simulations for small samples show that R sub Bt is better than the method of moments estimator for all alpha and as good as the mle for small alpha in the sense of mean squared errors.
- Statistics and Probability