A new sufficient condition for identifiability of countably infinite mixtures

While identifiability of finite mixtures for a wide range of distributions has been studied by statisticians for decades, discussion on countably infinite mixtures is still limited. This article provides an sufficient condition by means of well-ordered sets and uniform convergence of series. It is then applied to revisit some examples for which the identifiability is well established and then explore the identifiability for several distribution families, including normal, gamma, Cauchy, noncentral <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\chi ^2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msup> <mrow> <mi mathvariant="italic">χ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </EquationSource> </InlineEquation>, multivariate normal distributions. Copyright Springer-Verlag Berlin Heidelberg 2014