Order Selection in a Finite Mixture of Birnbaum-Saunders Distributions

Abstract

One of the most significant and difficult problems in a mixture study is the selection of the number of components. In this paper, using a Monte Carlo study, we evaluate and compare the performance of several information criteria for selecting the number of components arising from a mixture of Birnbaum-Saunders distributions. In our comparison, we consider information criteria based on likelihood-based statistics and classification likelihood-based statistics. The performance of information criteria is determined based on the success rate in selecting the number of components. In the simulation study, we investigate the effect of degrees of separation, sample sizes, mixing proportions, and true model complexity on the performance of information criteria. Furthermore, we compare the performance of the proposed information criteria under unpenalized and penalized estimation. Finally, we discuss the performance of the proposed information criteria for a real data set.