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

Abdelhanid Hassairi; Gérard Letac

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arXiv · 2512.19303

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

Abdelhanid Hassairi·Gérard Letac

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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 $\R^n$ 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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Abdelhanid Hassairi, Gérard Letac. 2025-12-22. Simple Cubic Variance Functions on $\R^n$, Part one. https://arxiv.org/abs/2512.19303

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