Statistical Inference and Prediction for the Gompertz Distribution Based on Multiply Type-I Censored Data

Abstract

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

E‐Bayesian estimation for the parameters and hazard function of Gompertz distribution based on progressively type‐II right censoring with application

“…Many authors discussed the GD, for example, Mohie El‐Din and Abu‐Moussa 7 introduced statistical inference for the GD based on multiply type‐I censored data. Also, Mohie El‐Din et al 8 .…”

“…Many authors discussed the GD, for example, Mohie El-Din and Abu-Moussa 7 introduced statistical inference for the GD based on multiply type-I censored data. Also, Mohie El-Din et al 8 an estimation and prediction for the GD using the Generalized hybrid censored data.…”