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arXiv · 2409.18421

Moment varieties of the inverse Gaussian and gamma distributions are nondefective

Oskar Henriksson·Kristian Ranestad·Lisa Seccia·Teresa Yu
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Abstract

We show that the parameters of a $k$-mixture of inverse Gaussian or gamma distributions are algebraically identifiable from the first $3k-1$ moments, and rationally identifiable from the first $3k+2$ moments. Our proofs are based on Terracini's classification of defective surfaces, careful analysis of the intersection theory of moment varieties, and a recent result on sufficient conditions for rational identifiability of secant varieties by Massarenti--Mella.

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Oskar Henriksson, Kristian Ranestad, Lisa Seccia, Teresa Yu. 2024-09-27. Moment varieties of the inverse Gaussian and gamma distributions are nondefective. https://doi.org/10.1016/j.jsc.2025.102460

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