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Expressions for Rényi and Shannon entropies for multivariate distributions

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  • Zografos, K.
  • Nadarajah, S.
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    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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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 71 (2005)
    Issue (Month): 1 (January)
    Pages: 71-84

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    Handle: RePEc:eee:stapro:v:71:y:2005:i:1:p:71-84

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    Related research

    Keywords: Elliptically contoured distributions Rényi entropy Shannon entropy;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Zografos, K., 1999. "On Maximum Entropy Characterization of Pearson's Type II and VII Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 67-75, October.
    2. Golan, Amos & Perloff, Jeffrey M., 2002. "Comparison of maximum entropy and higher-order entropy estimators," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 195-211, March.
    3. Peddada, Shyamal Das & Richards, Donald St. P., 1991. "Entropy inequalities for some multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 202-208, October.
    4. G. Aulogiaris & K. Zografos, 2004. "A maximum entropy characterization of symmetric Kotz type and Burr multivariate distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 13(1), pages 65-83, June.
    5. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers 1488, Iowa State University, Department of Economics.
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    Cited by:
    1. 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.
    2. 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.
    3. Bhattacharya, Bhaskar, 2006. "Maximum entropy characterizations of the multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1272-1283, July.
    4. 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.
    5. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2005. "Dynamic generalized information measures," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 85-98, January.
    6. 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.

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