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Lithuanian Mathematical Journal

, Volume 58, Issue 4, pp 441–456 | Cite as

Characterization and classification of multiple stable Tweedie models

  • Célestin C. Kokonendji
  • Cyrille C. Moypemna Sembona
Article
  • 19 Downloads

Abstract

Extending normal stable Tweedie models, the multiple stable Tweedie (MST) models are recently introduced as a huge class of multivariate distributions. They are composed by a fixed univariate stable Tweedie variable having a positive mean domain and random variables that, given the fixed one, are real independent stable Tweedie variables, possibly different, with the same dispersion parameter equal to the fixed component.Within the framework of exponential dispersion models, we completely prove the characterization of the MST models through their variance functions under steepness property. Thereforewe deduce a new classification of the Poisson-MST, gamma-MST, noncentral-gamma-MST, and inverse-Gaussian-MST families, where each of them contains one element of the normal stable Tweedie models, namely normal-Poisson, normal-gamma (or gamma-Gaussian), normal-noncentral-gamma, and normal-inverse-Gaussian distributions, respectively.

Keywords

multivariate exponential dispersion model steepness symmetric matrix variance function 

MSC

62H05 62E10 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Célestin C. Kokonendji
    • 1
  • Cyrille C. Moypemna Sembona
    • 2
  1. 1.Laboratoire de Mathématiques de Besançon – UMR 6623 CNRS-UFCUniversité Bourgogne Franche-ComtéBesançon cedexFrance
  2. 2.Département de MathématiquesUniversité de BanguiBanguiCentral African Republic

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