This article considers the Bayesian and non-Bayesian approaches for estimating the Gompertz distribution parameters and the acceleration factor when the data are obtained under the Type II censoring scheme from a step-stress partially accelerated life test. Both the maximum likelihood and Bayesian estimators of the model parameters are derived. The posterior means and posterior variances are derived under the squared error (SE) loss function using Lindley's approximation procedure. The advantage of this proposed procedure is shown. Monte Carlo simulations are performed under different samples sizes and different parameter values for investigating and comparing the proposed methods of estimation. A non-informative prior on the model parameters is used to make the comparison more meaningful.
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