The log-Weibull-negative-binomial regression model under latent failure causes and presence of randomized activation schemes

Abstract

The purpose of this paper is to develop a Bayesian approach for the log-Weibull-negative-binomial regression model under latent failure causes and presence of a randomized activation mechanism. We assume the number of competing causes of the event of interest follows a negative binomial distribution while the latent lifetimes are assumed to follows a Weibull distribution. Markov chain Monte Carlo methods are used to develop a Bayesian approach. Model selection to compare the fitted models is discussed. Moreover, we develop case deletion influence diagnostics for the joint posterior distribution based on the ψ-divergence, which has several divergence measures as particular cases. The developed procedures are illustrated on artificial and real data sets.