An Information-Theoretic Approach for Multivariate Skew- t Distributions and Applications

Salah H. Abid, Uday J. Quaez and Javier E. Contreras-Reyes
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Salah H. Abid: Department of Mathematics, Education College, Al-Mustansiriya University, Baghdad 14022, Iraq
Uday J. Quaez: Department of Mathematics, Education College, Al-Mustansiriya University, Baghdad 14022, Iraq
Javier E. Contreras-Reyes: Instituto de Estadística, Facultad de Ciencias, Universidad de Valparaíso, Valparaíso 2360102, Chile

Mathematics, 2021, vol. 9, issue 2, 1-13

Abstract: Shannon and Rényi entropies are two important measures of uncertainty for data analysis. These entropies have been studied for multivariate Student- t and skew-normal distributions. In this paper, we extend the Rényi entropy to multivariate skew- t and finite mixture of multivariate skew- t (FMST) distributions. This class of flexible distributions allows handling asymmetry and tail weight behavior simultaneously. We find upper and lower bounds of Rényi entropy for these families. Numerical simulations illustrate the results for several scenarios: symmetry/asymmetry and light/heavy-tails. Finally, we present applications of our findings to a swordfish length-weight dataset to illustrate the behavior of entropies of the FMST distribution. Comparisons with the counterparts—the finite mixture of multivariate skew-normal and normal distributions—are also presented.

Keywords: skew- t; finite mixtures; skewness; heavy-tails; Shannon entropy; Rényi entropy; swordfish data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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