Hamiltonian Monte Carlo Method for Parameter estimation of the Additive Weibull distribution

The additive Weibull distribution published in reliability Uterature is a simple model based on adding two Weibull survival functions. This four-parameter model seems to be flexible enough for modeling lifetimes possessing bathtubshaped failure rate. Most research publications, however, have provided poor results when fitting this model to real data sets that exhibit bathtub-shaped failure rate. In this study, we exploit the Hamiltonian Monte Carlo and cross-entropy methods in order to reinforce and strengthen the traditional methods of statistical estimation. Our results show the superiority of the recommended estimation methods over the others when fitting additive Weibull model to a real data set.