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An Information-Theoretic Approach for Multivariate Skew-t Distributions and Applications
- Source :
- Mathematics, Vol 9, Iss 146, p 146 (2021), Mathematics; Volume 9; Issue 2; Pages: 146
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
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.
- Subjects :
- Multivariate statistics
General Mathematics
media_common.quotation_subject
skew-t
skewness
heavy-tails
01 natural sciences
Upper and lower bounds
Asymmetry
010305 fluids & plasmas
Rényi entropy
010104 statistics & probability
0103 physical sciences
Computer Science (miscellaneous)
finite mixtures
Statistical physics
0101 mathematics
Engineering (miscellaneous)
Mathematics
media_common
Shannon entropy
swordfish data
lcsh:Mathematics
Skew
lcsh:QA1-939
Symmetry (physics)
Distribution (mathematics)
Skewness
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 9
- Issue :
- 146
- Database :
- OpenAIRE
- Journal :
- Mathematics
- Accession number :
- edsair.doi.dedup.....f6bdc841ec1b484776f3d970326da3c9