Bayesian Inference for the Discrete Weibull Regression Model with Type-I Right Censored Data

Abstract

This study purposes the use of Bayesian estimation for the discrete Weibull regression under type-I right censored data. Moreover, we compared the performance of the maximum likelihood estimation and the Bayesian estimation with uniform noninformative priors and informative priors using the random walk Metropolis algorithm. A simulation study was conducted to compare the performance of three different estimation methods using mean square error with three types of data: excessive zeros data, under-dispersion data, and over-dispersion data. A real dataset is analyzed to see how the model works in practice. The results from both the simulation study and a real data application showed that the maximum likelihood estimation and the Bayesian estimation with informative priors are both appropriate for the discrete Weibull regression under type-I right censored data in the cases of excessive zeros and under-dispersion. However, the Bayesian estimation with informative priors is more appropriate for the discrete Weibull regression under type-I right censored data than other methods in the case of over-dispersion.