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

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Keywords

  • Multivariate Exponential Dispersion Model
  • Regular Variation Karamata Representation