A note on the prior parameter choice in finite mixture models of distributions from exponential families

This work presents a new scheme to obtain the prior distribution parameters in the framework of Rufo et al. (Comput Stat 21:621–637, 2006). Firstly, an analytical expression of the proposed Kullback–Leibler divergence is derived for each distribution in the considered family. Therefore, no previous simulation technique is needed to estimate integrals and thus, the error related to this procedure is avoided. Secondly, a global optimization algorithm based on interval arithmetic is applied to obtain the prior parameters from the derived expression. The main advantage by using this approach is that all solutions are found and rightly bounded. Finally, an application comparing this strategy with the previous one illustrates the proposal.