The zero-truncated negative binomial distribution as a failure model from the Bayesian approach

Abstract

The zero-truncated negative binomial distribution is considered as a failure model from the Bayesian point of view. It is assumed that the location parameter is a stochastic variable with beta as its prior distribution. Under this assumption Bayes estimators are derived for the location parameter and reliability function. By means of Monte Carlo Simulation the minimum variance unbiased estimators (MVUEs) for the parameter and reliability function are compared to the corresponding Bayes estimators.