Abstract
A sufficient condition is given for a countable mixture to be identifiable provided that the supports of mixing distributions are well-ordered sets for a total ordering of the parameter space. The identifiability of some countable mixtures of loggamma distributions and that of some countable mixtures of reversed log-gamma distributions are studied. Both classes of all finite mixtures of log-gamma distributions and all finite mixtures of reversed log-gamma distributions are shown to be identifiable as special cases.
