A Selective Overview of SkewElliptical and Related Distributions and of Their Applications Within the context of flexible parametric families of distributions, much work has been dedicated in recent years to the theme of skewsymmetric distributions, or symmetrymodulated distributions, as we prefer to call them. The present contribution constitutes a review of this area, with special emphasis on multivariate skewelliptical families, which represent the subset with more immediate impact on applications. After providing background information of the distribution theory aspects, we focus on the aspects more relevant for applied work. The exposition is targeted to nonspecialists in this domain, although some general knowledge of probability and multivariate statistics is assumed. Given this aim, the mathematical profile is kept to the minimum required.

MIXANDMIX: numerical techniques for the computation of empirical spectral distributions of population mixtures The MIXANDMIX (mixtures by Anderson mixing) tool for the computation of the empirical spectral distribution of random matrices generated by mixtures of populations is described. Within the population mixture model the mapping between the population distributions and the limiting spectral distribution can be obtained by solving a set of systems of nonlinear equations, for which an efficient implementation is provided. The contributions include a method for accelerated fixed point convergence, a homotopy continuation strategy to prevent convergence to nonadmissible solutions, a blind nonuniform grid construction for effective distribution support detection and approximation, and a parallel computing architecture. Comparisons are performed with available packages for the single population case and with results obtained by simulation for the more general model implemented here. Results show competitive performance and improved flexibility.