Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring
In this paper, the Bayesian approach is applied to the estimation problem in the case of step stress partially accelerated life tests with two stress levels and type-I censoring. Gompertz distribution is considered as a lifetime model. The posterior means and posterior variances are derived using the squared-error loss function. The Bayes estimates cannot be obtained in explicit forms. Approximate Bayes estimates are computed using the method of Lindley [D.V. Lindley, Approximate Bayesian methods, Trabajos Estadistica 31 (1980), pp. 223-237]. The advantage of this proposed method is shown. The approximate Bayes estimates obtained under the assumption of non-informative priors are compared with their maximum likelihood counterparts using Monte Carlo simulation.
gompertz distribution acceleration factor type-i censoring posterior mean posterior variance squared-error loss function non-informative priors maximum likelihood monte carlo simulation bayesian estimation step-stress test lindley's approximation