{"ID":2826229,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.19303","arxiv_id":"2512.19303","title":"Simple Cubic Variance Functions on $\\R^n$, 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 $\\R^n$ 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.","short_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 pap...","url_abs":"https://arxiv.org/abs/2512.19303","url_pdf":"https://arxiv.org/pdf/2512.19303v1","authors":"[\"Abdelhanid Hassairi\",\"Gérard Letac\"]","published":"2025-12-22T11:46:51Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}