title: ON IDENTIFIABILITY OF MIXTURES OF INDEPENDENT DISTRIBUTION LAWS, .
abstract: We consider representations of a joint distribution law of a family of categorical random variables (i.e., a multivariate categorical variable) as a mixture of independent distribution laws (i.e.distribution laws according to which random variables are mutually independent). For infinite families of random variables, we describe a class of mixtures with identifiable mixing measure. This class is interesting from a practical point of view as well, as its structure clarifies principles of selecting a "good" finite family of random variables to be used in applied research. For finite families of random variables, the mixing measure is never identifiable; however, it always possesses a number of identifiable invariants, which provide substantial information regarding the distribution under consideration.
authors.affiliation: Duke University, Dept. of Biology, Benfey Lab Durham, 27708 NC, 27708, USA.
authors.forename: Mikhail
authors.initials: M
authors.lastname: Kovtun
authors.affiliation: Center for Population Health and Aging Durham, 27708 NC, USA.
authors.forename: Igor
authors.initials: I
authors.lastname: Akushevich
authors.affiliation: Center for Population Health and Aging Durham, 27708 NC, USA.
authors.forename: Anatoliy
authors.initials: A
authors.lastname: Yashin
keywords: Latent structure analysis; identifiability; mixed distributions; moment problem