Media Internal Modeling without Copulas: The Beauty of Multivariates Thorin Classes

Internal Modeling without Copulas: The Beauty of Multivariates Thorin Classes

uploaded September 7, 2021 Views: 24 Comments: 0 Marked favorite: 0
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The generalized gamma convolution class of distribution appeared in Thorin's work while looking for the infinite divisibility of the log-Normal and Pareto distributions. Although these distributions have been extensively studied in the univariate case, the multivariate case and the additive risk factor structures that can arise from it have received little interest in the literature. Furthermore, only one projection procedure for the univariate case was recently constructed, and no estimation procedure are available. By expending the densities of multivariate generalized gamma convolutions into a tensorized Laguerre basis, we bridge the gap and provide performant estimations procedures for both the univariate and multivariate cases. We provide some insights about performance of these procedures, and a convergent series for the density of multivariate gamma convolutions, which is shown to be more stable than Moshopoulos's and Mathai's univariate series. We furthermore discuss some examples.

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