Bayesian analysis of survival data using the Rayleigh model and linex loss

Based on right censored data this paper presents the Bayes estimators for some lifetime distribution parameters such as the mean survival time, the hazard function and the survival distribution function, using the noninformative and informative prior distributions for theta. These estimators are derived using both the squared error loss function and Varian's asymmetric linear-exponential (linex) loss function. A hierarchical approach is followed when the hyperparameters of the conjugate gamma prior are unknown, which results in the use of the F-distribution as a prior for theta. A practical example illustrates the use of the non-informative and F priors under the two loss functions, as well as the prediction of the lifetime of a future observation/patient, for the case of unknown hyperparameters.