Comparison on the Bayesian Estimation of Gompertz Distribution Based on Type I Censored Data

Abstract

The paper depicts assessment of the Bayesian methodology utilizing Gaussian quadrature formulas and Markov Chain Monte Carlo of the Gompertz distribution based on type I censored data with two loss functions, the Square Error loss function and the Linear Exponential loss function. In Markov Chain Monte Carlo, the full conditional distributions for the scale and shape parameters, survival and hazard functions are acquired by means Gibbs sampling and Metropolis- Hastings algorithm. The strategies for the Bayesian methodology are contrasted with maximum likelihood estimation regarding the Mean Square Error (MSE) to decide the best assessing of the scale and shape parameters, survival and hazard functions of the Gompertz distribution based on type I censored data.

Keywords: Gompertz distribution, Bayesian estimation, Type I censored data, Gaussian Quadrature Formulas, Markov Chain Monte Carlo.