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Multivariate Liouville Distributions, IV

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  • Gupta, R. D.
  • Richards, D. S. P.

Abstract

We define a class of distributions, containing the classical Dirichlet and Liouville distributions, in which the random variables take values in a locally compact Abelian group or semigroup. These generalizations retain many properties of the Dirichlet and Liouville distributions, including properties of the marginal and conditional distributions and regression functions. We present a number of examples illustrating the general theory.

Suggested Citation

  • Gupta, R. D. & Richards, D. S. P., 1995. "Multivariate Liouville Distributions, IV," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 1-17, July.
  • Handle: RePEc:eee:jmvana:v:54:y:1995:i:1:p:1-17
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    Citations

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    Cited by:

    1. Edward Hoyle & Levent Ali Menguturk, 2020. "Generalised Liouville Processes and their Properties," Papers 2003.11312, arXiv.org, revised May 2020.
    2. Gupta, Rameshwar D. & Richards, Donald St. P., 2002. "Moment Properties of the Multivariate Dirichlet Distributions," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 240-262, July.
    3. Bhattacharya, P. K. & Burman, Prabir, 1998. "Semiparametric Estimation in the Multivariate Liouville Model," Journal of Multivariate Analysis, Elsevier, vol. 65(1), pages 1-18, April.
    4. Hoyle, Edward & Hughston, Lane P. & Macrina, Andrea, 2011. "Lévy random bridges and the modelling of financial information," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 856-884, April.
    5. Ongaro, A. & Migliorati, S., 2013. "A generalization of the Dirichlet distribution," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 412-426.
    6. Letac, Gérard & Massam, Hélène & Richards, Donald, 2001. "An Expectation Formula for the Multivariate Dirichlet Distribution," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 117-137, April.
    7. Elena Hadjicosta & Donald Richards, 2020. "Integral transform methods in goodness-of-fit testing, II: the Wishart distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1317-1370, December.

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