Weighted balanced loss function and estimation of the mean time to failure

Abstract

Abstract The purpose of this paper is to consider estimation of the mean time to failure using loss functions that reflect both of fit and precision of estimation. We show how this can be done using balanced loss functions (BLF) of the type introduced in Zellner (1994) and weighted balanced loss function (WBLF) introduced in this paper. Optimal point estimates relative to BLF and WBLF are shown to be a compromise between usual Bayesian and non-Bayesian estimates. Using diffuse and informative priors, posterior expected losses associated with alternative estimates are evaluated and compared. Keywords: Failure time analysisBayesian and non-Bayesian estimationBalanced Loss Functions