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Simulations of full multivariate Tweedie with flexible dependence structure. (English) Zbl 1348.65019
Summary: 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.

MSC:
65C60 Computational problems in statistics (MSC2010)
62H99 Multivariate analysis
60E07 Infinitely divisible distributions; stable distributions
91B30 Risk theory, insurance (MSC2010)
Software:
R; SuppDists; Tweedie
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