Motivated by previous work on moment varieties for Gaussian distributions and their mixtures, we study moment varieties for two other statistically important two-parameter distributions: the inverse Gaussian and gamma distributions. In particular, we realize the moment varieties as determinantal varieties and find their degrees and singularities. We also provide computational evidence for algebraic identifiability of mixtures, and study the identifiability degree and Euclidean distance degree.

翻译：受先前关于高斯分布及其混合分布的矩簇研究启发，本文研究了另外两种重要二参数统计分布的矩簇：逆高斯分布与伽马分布。具体而言，我们将矩簇实现为行列式簇，并确定了其次数与奇异性。同时，我们为混合分布的可代数辨识性提供了计算证据，并研究了可辨识度与欧几里得距离度。