Simple Cubic Variance Functions on \Rⁿ, Part one

2025/12/22 by Abdelhanid Hassairi, Hassairi, Abdelhanid, Gérard Letac +1
Mathematics · #Mathematical functions and polynomials #Advanced Mathematical Identities #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.2512.19303

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 \Rⁿ and to degree three is the subject of this paper. Keywords: Actions of the group GL(n+1,\R), classification of natural exponential families, multivariate Lagrange formula. variance functions.

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