Open Access
2021 Estimation of multivariate generalized gamma convolutions through Laguerre expansions.
Oskar Laverny, Esterina Masiello, Véronique Maume-Deschamps, Didier Rullière
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Electron. J. Statist. 15(2): 5158-5202 (2021). DOI: 10.1214/21-EJS1918


The generalized gamma convolutions class of distributions 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 dependence 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 procedures are available. By expanding the densities of multivariate generalized gamma convolutions into a tensorized Laguerre basis, we bridge the gap and provide performant estimation 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 Moschopoulos’s and Mathai’s univariate series. We furthermore discuss some examples.


We thank the referees for all the important remarks they made and all resulting improvement to the paper.


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Oskar Laverny. Esterina Masiello. Véronique Maume-Deschamps. Didier Rullière. "Estimation of multivariate generalized gamma convolutions through Laguerre expansions.." Electron. J. Statist. 15 (2) 5158 - 5202, 2021.


Received: 1 April 2021; Published: 2021
First available in Project Euclid: 8 December 2021

Digital Object Identifier: 10.1214/21-EJS1918

Primary: 60E07 , 62H12
Secondary: 60E10

Keywords: estimation , Infinite divisibility , Laguerre’s basis , Multivariate generalized gamma convolutions , Thorin’s measure

Vol.15 • No. 2 • 2021
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