Mixtures of power series distributions: identifiability via uniqueness in problems of moments. (English) Zbl 1432.60027
Summary: We treat the identifiability problem for mixtures involving power series distributions. Applying an idea of T. Sapatinas [Ann. Inst. Stat. Math. 47, No. 3, 447–459 (1995; Zbl 0845.62014)] we prove and elaborate that a mixture distribution is identifiable if a certain Stieltjes problem of moments has a unique solution while a non-uniqueness leads to a non-identifiable mixture. We describe explicitly models of identifiable mixtures and models of non-identifiable mixtures. Illustrative examples and comments on related questions are also given.
Keywords:
power series distributions; mixtures of distributions; identifiability; non-identifiability; Stieltjes problem of moments; uniqueness; non-uniquenessCitations:
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