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Expressions for Rényi and Shannon entropies for multivariate distributions

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  • Zografos, K.
  • Nadarajah, S.

Abstract

Exact forms of Rényi and Shannon entropies are determined for several multivariate distributions, including multivariate t, multivariate Cauchy, multivariate Pearson type VII, multivariate Pearson type II, multivariate symmetric Kotz type, multivariate logistic, multivariate Burr, multivariate Pareto type I, multivariate Pareto type II, multivariate Pareto type III, multivariate Pareto type IV, Dirichlet, inverted Dirichlet, multivariate Liouville, multivariate exponential, multivariate Weinman exponential, multivariate ordered Weinman exponential, bivariate gamma exponential, bivariate conditionally specified exponential, multivariate Weibull and multivariate log-normal. Monotonicity properties of Rényi and Shannon entropies for these distributions are also studied. We believe that the results presented here will serve as an important reference for scientists and engineers in many areas.

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  • Zografos, K. & Nadarajah, S., 2005. "Expressions for Rényi and Shannon entropies for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 71-84, January.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:1:p:71-84
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    2. Nathan Lassance & Frédéric Vrins, 2021. "Minimum Rényi entropy portfolios," Annals of Operations Research, Springer, vol. 299(1), pages 23-46, April.
    3. Ebrahimi, Nader & Jalali, Nima Y. & Soofi, Ehsan S., 2014. "Comparison, utility, and partition of dependence under absolutely continuous and singular distributions," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 32-50.
    4. Carol Alexander & José María Sarabia, 2012. "Quantile Uncertainty and Value‐at‐Risk Model Risk," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1293-1308, August.
    5. W. V. Félix de Lima & A. D. C. Nascimento & G. J. A. Amaral, 2021. "Entropy-based pivotal statistics for multi-sample problems in planar shape," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 153-178, March.
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    7. Zografos, K., 2008. "On Mardia's and Song's measures of kurtosis in elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 858-879, May.
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    10. Vuong, Q.N. & Bedbur, S. & Kamps, U., 2013. "Distances between models of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 24-36.
    11. Burkschat, M. & Kamps, U. & Kateri, M., 2010. "Sequential order statistics with an order statistics prior," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1826-1836, September.
    12. Nader Ebrahimi & S.N.U.A. Kirmani & Ehsan S. Soofi, 2011. "Predictability of operational processes over finite horizon," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 531-545, September.
    13. Withers, Christopher S. & Nadarajah, Saralees, 2011. "Estimates of low bias for the multivariate normal," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1635-1647, November.
    14. Contreras-Reyes, Javier E., 2014. "Asymptotic form of the Kullback–Leibler divergence for multivariate asymmetric heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 200-208.
    15. Daya K. Nagar & Saralees Nadarajah & Idika E. Okorie, 2017. "A New Bivariate Distribution with One Marginal Defined on the Unit Interval," Annals of Data Science, Springer, vol. 4(3), pages 405-420, September.

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