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Research Article Open access CC BY 4.0

Bayesian Estimation and Prediction of Discrete Gompertz Distribution

M. A. Hegazy, R. E. Abd El-Kader, A. A. EL-Helbawy, G. R. AL-Dayian

Journal of Advances in Mathematics and Computer Science · pp. 1–21 · Published 18 Mar 2021

10.9734/jamcs/2021/v36i230335

Abstract

In this paper, Bayesian inference is used to estimate the parameters, survival, hazard and alternative hazard rate functions of discrete Gompertz distribution. The Bayes estimators are derived under squared error loss function as a symmetric loss function and linear exponential loss function as an asymmetric loss function. Credible intervals for the parameters, survival, hazard and alternative hazard rate functions are obtained. Bayesian prediction (point and interval) for future observations of discrete Gompertz distribution based on two-sample prediction are investigated. A numerical illustration is carried out to investigate the precision of the theoretical results of the Bayesian estimation and prediction on the basis of simulated and real data. Regarding the results of simulation seems to perform better when the sample size increases and the level of censoring decreases. Also, in most cases the results under the linear exponential loss function is better than the corresponding results under squared error loss function. Two real lifetime data sets are used to insure the simulated results.

Gompertz distribution Bayes estimators squared error loss function linear exponential loss function credible intervals Bayesian prediction Monte Carlo simulation

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