This paper considers empirical Bayes (EB) squared-error-loss estimations of mean lifetime, variance and reliability function for failure-time distributions belonging to an exponential family, which includes gamma and Weibull distributions as special cases. EB estimators are proposed when the prior distribution of the lifetime parameter is completely unknown but has a compact (known or unknown) support. Asymptotic optimality and rates of convergence of these estimators are investigated. The rates established here under the compact support restriction are better than the polynomial rates of convergence obtained previously.



Les auteurs abordent l'estimation bayesienne empirique, sous fonction de perte quadratique, de la duree de vie moyenne, de la variance et de la fiabilite de distributions de temps de panne appartenant a une famille exponentielle, comme e'est le cas pour les lois gamma ou de Weibull par exemple. lls proposent des estimateurs de Bayes empiriques pour les situations ou la loi a priori du parametre de duree de vie est completement inconnue, sauf pour le fait qu'elle possede un support compact (precise ou non). lls etudient I'optimalite asymptotique et les taux de convergence de tels estimateurs. Les taux qu'ils obtiennent en postulant la compacite du support sont meilleurs que les taux de convergence polynomiaux dej a connus.

Empirical bayes estimation of reliability characteristics for an exponential family

Bayesian estimation for shifted exponential distributions

We study empirical Bayes estimation of reliability in a lifetime distribution having probability density f(y|θ) = αyαν−1 exp(−yα/θ)/[Γ(ν)θν], where 0   1 and ν* = max(1, ν) cases), where n is the number of past data available when the estimation problem is considered.

Empirical Bayes Estimation of Reliability in a Positive Exponential Family

This paper discusses the Bayesian reliability analysis for the two-parameter exponential distribution on the basis of the life tests that are terminated after a pre assigned number of failures, when the prior distribution of the location parameter, given the scale, is assumed to be exponential, while the scale parameter is assumed to have an inverse Gaussian prior distribution. The usual assumption of the squared error loss function is also made. A situation dealing with attribute life testing is also considered.

Samir K. Battacharya

Papers

Bayesian reliability analysis for the two-parameter exponential distribution