Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data

In this paper, the statistical inference for the Gompertz distribution based on generalized progressively hybrid censored data is discussed. The estimation of the parameters for Gompertz distribution is discussed using the maximum likelihood method and the Bayesian methods under different loss functions. The existence and uniqueness of the maximum likelihood estimation are proved. The point and interval Bayesian predictions for unobserved failures from the same sample and that from the future sample are derived. The Monte Carlo simulation is applied to compare the proposed methods. A real data example is used to apply the methods of estimation and to construct the prediction intervals. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.