Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring

Abstract

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.

Keywords:

• Bayesian estimation
• step-stress test
• acceleration factor
• Gompertz distribution
• maximum likelihood
• squared-error loss function
• non-informative priors
• posterior mean
• posterior variance
• type-I censoring
• Lindley's approximation
• Monte Carlo simulation

MSC :

• 62N01
• 62N05

Acknowledgements

The author would like to thank both the Deanship of Scientific Research and the Research Center, College of Science, King Saud University. The author would also like to thank the editors and the referees for their carefully reading of the manuscript, and for their valuable comments and suggestions.

Additional information

Notes on contributors

Ali. A. Ismail

Also: Department of Statistics, Faculty of Economics & Political Science, Cairo University, Giza, Egypt.