Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data

Abstract

Bayes and frequentist estimators are obtained for the two-parameter Gompertz distribution (GD), as well as the reliability and hazard rate functions, using progressive first-failure censoring plan. We have examined Bayes estimates under symmetric and asymmetric loss functions. We show that the Bayes estimates relative to asymmetric loss function includes the maximum likelihood estimate (MLE) and other Bayes estimates as special cases. This is done using the conjugate prior for the scale parameter and discrete prior for the shape parameter. It has been seen that the Bayes estimators are obtained in closed form. Also, based on this new censoring scheme, exact and approximate confidence intervals as well as exact confidence region for the parameters of GD are developed. A practical example using simulated data set was used for illustration. Finally, to assess the performance of the proposed estimators, numerical results using Monte Carlo simulation study were reported.