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Characterization of infinitely divisible multivariate gamma distributions

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  • Griffiths, R. C.

Abstract

A particular class of p-dimensional exponential distributions have Laplace transforms I + VT-1, V positive definite or positive semi-definite and T = diagonal (t1,..., tp). A characterization is given of when these Laplace transforms are infinitely divisible.

Suggested Citation

  • Griffiths, R. C., 1984. "Characterization of infinitely divisible multivariate gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 13-20, August.
    • Handle: RePEc:eee:jmvana:v:15:y:1984:i:1:p:13-20
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    Citations

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    Cited by:

    1. Boris Buchmann & Benjamin Kaehler & Ross Maller & Alexander Szimayer, 2015. "Multivariate Subordination using Generalised Gamma Convolutions with Applications to V.G. Processes and Option Pricing," Papers 1502.03901, arXiv.org, revised Oct 2016.
    2. Eisenbaum, Nathalie & Kaspi, Haya, 2009. "On permanental processes," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1401-1415, May.
    3. Pérez-Abreu, Victor & Stelzer, Robert, 2014. "Infinitely divisible multivariate and matrix Gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 155-175.
    4. Das, Sourish & Dey, Dipak K., 2010. "On Bayesian inference for generalized multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1492-1499, October.
    5. Jesper Møller & Ege Rubak, 2010. "A Model for Positively Correlated Count Variables," International Statistical Review, International Statistical Institute, vol. 78(1), pages 65-80, April.
    6. Bobecka, Konstancja & Wesolowski, Jacek, 2004. "Multivariate Lukacs theorem," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 143-160, November.
    7. Denuit, Michel & Lu, Yang, 2020. "Wishart-Gamma mixtures for multiperil experience ratemaking, frequency-severity experience rating and micro-loss reserving," LIDAM Discussion Papers ISBA 2020016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.

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