STATISTICAL INFERENCE AND PREDICTION FOR THE GOMPERTZ DISTRIBUTION BASED ON MULTIPLY TYPE-I CENSORED DATA

In this paper, we make a statistical inference for the Gompertz distribution based on multiply Type-I censoreddata, where we determine a censoring time point for each unit in the life time test. Estimation of the parameters is obtainedusing maximum likelihood method and Bayesian method, also the asymptotic condence intervals for the parameters areconstructed based on the approximate of the Fisher information matrix. The necessary condition for existence and uniquenessof the maximum likelihood estimators is discussed. The Bayesian estimates are obtained depending on the squared error lossfunction, linear exponential loss function and the generalized entropy loss function. The One-sample Bayesian predictionintervals are constructed for the unobserved lifetimes in the same sample. A real data example is presented to illustrate themethods of inference developed here. Finally, the simulation study is executed to compare the performance of the proposedmethods.