Simple Cubic Variance Functions on ${\mathbb{R}}^n$, Part one

Abstract

The classification of natural exponential families started with the paper \cite {Morri} where Carl Morris unifies six very familiar families by the fact that their variance functions are polynomials of degree less or equal to two. Extension of this classification to ${\mathbb{R}}^n$ and to degree three is the subject of this paper. Keywords: Actions of the group $GL(n+1,\mathbb{R})$, classification of natural exponential families, multivariate Lagrange formula. variance functions.

46 pages