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：受高斯分布及其混合矩簇先前研究的启发，本文针对两个在统计学中重要的两参数分布——逆高斯分布与伽马分布——系统研究了其矩簇。我们特别将矩簇实现为行列式簇，并确定了它们的次数和奇异性。此外，我们提供了混合模型代数可辨识性的计算证据，同时研究了辨识度与欧几里得距离度。