Non-exponential families of distributions
The problem discussed is whether a given set \({\mathcal P}\) of mutually equivalent probability distributions constitutes an exponential family or not. As an alternative to the well known characterization by linear independence an analytic method is pointed out which allows one to demonstrate in a relatively easy way that many familiar classes of distributions (e.g. Cauchy-, \(t_ n\)-, logistic-) are not exponential families.
non-exponential families of distributions
mutually equivalent probability distributions
scientific article; zbMATH DE number 3996844