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On Maximum Entropy Characterization of Pearson's Type II and VII Multivariate Distributions

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  • Zografos, K.

Abstract

In this paper a characterization is presented for Pearson's Type II and VII multivariate distributions by means of the maximum entropy principle. It is shown that within the class of multivariate distributions, that satisfy appropriate constraints expressed by mean values, the Pearson Type II and VII distributions maximize the Shannon entropy.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:71:y:1999:i:1:p:67-75
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    References listed on IDEAS

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    1. Silviu Guiasu, 1990. "A classification of the main probability distributions by minimizing the weighted logarithmic measure of deviation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 269-279, June.
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    Cited by:

    1. Ebrahimi, Nader & Soofi, Ehsan S. & Soyer, Refik, 2008. "Multivariate maximum entropy identification, transformation, and dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1217-1231, July.
    2. 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.
    3. Leonenko, Nikolaj & Seleznjev, Oleg, 2010. "Statistical inference for the [epsilon]-entropy and the quadratic Rényi entropy," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1981-1994, October.
    4. Ebrahimi, Nader & Kirmani, S.N.U.A. & Soofi, Ehsan S., 2007. "Multivariate dynamic information," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 328-349, February.
    5. Bhattacharya, Bhaskar, 2006. "Maximum entropy characterizations of the multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1272-1283, July.
    6. 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.
    7. Andai, Attila, 2009. "On the geometry of generalized Gaussian distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 777-793, April.
    8. Villa, Cristiano & Rubio, Francisco J., 2018. "Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 197-219.
    9. Castilla, Elena & Zografos, Konstantinos, 2022. "On distance-type Gaussian estimation," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. 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.
    11. 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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