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Entropy indicates a measure of information contained in a complex system, and its estimation continues to receive ongoing focus in the case of multivariate data, particularly that on the unit simplex. Oftentimes the Dirichlet distribution is employed as choice of prior in a Bayesian framework conjugate to the popular multinomial likelihood with K distinct classes, where consideration of Shannon- and Tsallis entropy is of interest for insight detection within the data on the simplex. However, this prior choice only accounts for negatively correlated data, therefore this paper incorporates previously unconsidered mixtures of Dirichlet distributions as potential priors for the multinomial likelihood which addresses the drawback of negative correlation. The power sum functional, as the product moment of the mixture of Dirichlet distributions, is of direct interest in the multivariate case to conveniently access the Tsallis- and other generalized entropies that is incorporated within an estimation perspective of the posterior distribution using real economic data. A prior selection method is implemented to suggest a suitable prior for the consideration of the practitioner; empowering the user in future for consideration of suitable priors incorporating entropy within the estimation environment as well as having the option of certain mixture of Dirichlet distributions that may require positive correlation. [ABSTRACT FROM AUTHOR]

Finite mixture models have recently been considered for analyzing positive support economical data streams with non-normal features. In this paper, a new mixture model based on the novel class of generalized Birnbaum–Saunders distributions is proposed to enhance strength and flexibility in modeling heterogeneous lifetime data. Some characteristics and properties of this mixture model are outlined. By presenting a convenient hierarchical representation, a mathematically elegant and computationally tractable EM-type algorithm is adopted for computing maximum likelihood estimates. Theoretical formulae of well-known risk measures referring to the class of generalized Birnbaum–Saunders distributions are derived. Finally, the utility of the postulated methodology is illustrated with some real-world data examples. [ABSTRACT FROM AUTHOR]