Estimation of some lifetime parameters of generalized Gompertz distribution under progressively type-II censored data

In this paper, the estimation of parameters of a three-parameter generalized Gompertz distribution based on progressively type-II right censored sample is studied. These methods include the maximum likelihood estimators (MLEs), and Bayesian estimators. Approximate confidence intervals for the unknown parameters as well as reliability function, hazard function and coefficient of variation are constructed based on the s-normal approximation to the asymptotic distribution of MLEs, and log-transformed MLEs. Furthermore, two bootstrap confidence intervals are proposed. Several Bayesian estimates are obtained against different symmetric and asymmetric loss functions such as squared error, LINEX and general entropy. Based on theses loss functions, under gamma priors distributions, Bayes estimates of the unknown parameters and the corresponding credible intervals are obtained by using the Gibbs within Metropolis–Hasting samplers procedure. Finally, a real data set is analyzed to illustrate the proposed methods.