  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.
