Modeling distributions on a bounded support via finite mixtures of mode-parameterized beta and gamma densities

This paper address the problem of estimating a density, defined on a bounded interval, exploiting a general and natural form of finite mixture of distributions. To this end, subclasses of unimodal beta and gamma densities are used as components in the mixture. These belong to the Pearson family of curves, whose definition consent mode-parameterized densities. The mode is the natural parameter since mixtures of distributions are strictly related to the concept of multimodality. The EM algorithm for maximum likelihood estimation of the mixture parameters, is also described. For this algorithm, the choice of good starting values plays an important role. Here we propose a simple and ad hoc initialization strategy, based on bump-hunting; performance, in comparison with random initialization, is also evaluated by some simulation experiments. Finally, two real data sets are considered, in order to appreciate the advantages of the adopted parameterization for both components.