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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

A Convergence Theorem for Bivariate Exponential Dispersion Models

Lila Ricci1 and Gabriela Boggio2
  • 1 Universidad Nacional de Mar del Plata, Argentina
  • 2 Universidad Nacional de Rosario, Argentina

Abstract

Multivariate exponential dispersion models (MEDMs) were defined in 2013 by Jørgensen and Martínez. A particular case of MEDM is the bivariate Gamma model; in this article we prove that, under certain conditions, this is a limit distribution for MEDM generated by bivariate regularly varying measures, extending a previous result given by the aforementioned authors for the univariate case. As necessary tools for proving the main result, we use bivariate regularly varying functions and bivariate regularly varying measures; we also state a bivariate version of Tauberian Karamata’s theorems and a particular Karamata representation of bivariate slowly varying functions.

Journal of Mathematics and Statistics
Volume 15 No. 1, 2019, 176-184

DOI: https://doi.org/10.3844/jmssp.2019.176.184

Submitted On: 16 May 2019 Published On: 25 July 2019

How to Cite: Ricci, L. & Boggio, G. (2019). A Convergence Theorem for Bivariate Exponential Dispersion Models. Journal of Mathematics and Statistics, 15(1), 176-184. https://doi.org/10.3844/jmssp.2019.176.184

Open AccessCopyright: © 2019 Lila Ricci and Gabriela Boggio. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Multivariate Exponential Dispersion Model
  • Regular Variation Karamata Representation