Bayes estimation of the linear hazard-rate model

In life testing, the failure-time distributions are often specified by choosing an appropriate hazard-rate function. The class of life-time distribution characterized by a linear hazard-rate includes the one-parameter exponential and Rayleigh distributions. Usually the parameters of the linear hazard-rate model are estimated by the method of least squares. This work is concerned with Bayes estimation of the two-parameters from a type-2 censored sample. Monte Carlo simulation is used to compare the Bayes risk of the regression estimator with the minimum Bayes risk. Discrete mixtures of decreasing failure rate distributions are known to have decreasing failure rates. The authors prove that the result holds for continuous mixtures as well