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Maximum entropy characterizations of the multivariate Liouville distributions

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  • Bhattacharya, Bhaskar

Abstract

A random vector X=(X1,X2,...,Xn) with positive components has a Liouville distribution with parameter [theta]=([theta]1,[theta]2,...,[theta]n) if its joint probability density function is proportional to , [theta]i>0 [R.D. Gupta, D.S.P. Richards, Multivariate Liouville distributions, J. Multivariate Anal. 23 (1987) 233-256]. Examples include correlated gamma variables, Dirichlet and inverted Dirichlet distributions. We derive appropriate constraints which establish the maximum entropy characterization of the Liouville distributions among all multivariate distributions. Matrix analogs of the Liouville distributions are considered. Some interesting results related to I-projection from a Liouville distribution are presented.

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  • Bhattacharya, Bhaskar, 2006. "Maximum entropy characterizations of the multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1272-1283, July.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1272-1283
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    References listed on IDEAS

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    1. 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;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 65-83, June.
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    Cited by:

    1. 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.

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