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Simulations of full multivariate Tweedie with flexible dependence structure

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Abstract

We employ a variables-in-common method for constructing multivariate Tweedie distributions, based on linear combinations of independent univariate Tweedie variables. The method lies on the convolution and scaling properties of the Tweedie laws, using the cumulant generating function for characterization of the distributions and correlation structure. The routine allows the equivalence between independence and zero correlation and gives a parametrization through given values of the mean vector and dispersion matrix, similarly to the Gaussian vector. Our approach leads to a matrix representation of multivariate Tweedie models, which permits the simulations of many known distributions, including Gaussian, Poisson, non-central gamma, gamma, and inverse Gaussian, both positively or negatively correlated.

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Acknowledgments

The authors would like to sincerely thank the editor, the associate editor as well as the anonymous referees for their valuable comments and suggestions which led to significant improvement in this article.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS-UFC, Université de Franche-Comté, UFR Sciences et Techniques, 16 route de Gray, 25030, Besançon Cedex, France

    Johann Cuenin & Célestin C. Kokonendji

  2. IMADA, University of Southern Denmark, Odense, Denmark

    Bent Jørgensen

Authors
  1. Johann Cuenin
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  2. Bent Jørgensen
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  3. Célestin C. Kokonendji
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Correspondence to Johann Cuenin.

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Cuenin, J., Jørgensen, B. & Kokonendji, C.C. Simulations of full multivariate Tweedie with flexible dependence structure. Comput Stat 31, 1477–1492 (2016). https://doi.org/10.1007/s00180-015-0617-3

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  • DOI: https://doi.org/10.1007/s00180-015-0617-3

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