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.

翻译：我们证明了$k$分量逆高斯或伽马混合分布的参数可通过前$3k-1$阶矩实现代数可识别，并通过前$3k+2$阶矩实现有理可识别。证明基于Terracini对缺陷曲面的分类、矩簇相交理论的精细分析，以及Massarenti--Mella最近关于割线簇有理可识别性充分条件的研究成果。