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

Author

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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)

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.

Suggested Citation

  • Salah H. Abid & Uday J. Quaez & Javier E. Contreras-Reyes, 2021. "An Information-Theoretic Approach for Multivariate Skew- t Distributions and Applications," Mathematics, MDPI, vol. 9(2), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:146-:d:478269
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    References listed on IDEAS

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    1. Contreras-Reyes, Javier E., 2015. "Rényi entropy and complexity measure for skew-gaussian distributions and related families," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 84-91.
    2. Reinaldo B. Arellano-Valle & Javier E. Contreras-Reyes & Marc G. Genton, 2013. "Shannon Entropy and Mutual Information for Multivariate Skew-Elliptical Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 42-62, March.
    3. Gilles Celeux & Gilda Soromenho, 1996. "An entropy criterion for assessing the number of clusters in a mixture model," Journal of Classification, Springer;The Classification Society, vol. 13(2), pages 195-212, September.
    4. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    5. Prates, Marcos Oliveira & Lachos, Victor Hugo & Barbosa Cabral, Celso Rômulo, 2013. "mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i12).
    6. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    7. Adelchi Azzalini & Giuliana Regoli, 2012. "Some properties of skew-symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 857-879, August.
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    Cited by:

    1. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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