A Convergence Theorem for Bivariate Exponential Dispersion Models
Lila Ricci1 & Gabriela Boggio2 Show affiliations
- Universidad Nacional de Mar del Plata, Argentina
- Universidad Nacional de Rosario, Argentina
Journal of Mathematics and Statistics, Volume 15, Issue 1, pp. 176–184 · doi.org/10.3844/jmssp.2019.176.184
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.
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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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