Parameter estimates and tests of fit for infinite mixther distrirutions

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Abstract
Al though mixtures form a rich class of probability models, they often present difficulties for statistical inference. Likelihood functions are sometimes unbounded at certain values of the parameters, and densities often have no closed form. These features complicate hoth maximum-likelihood estimation and tests of fit based on the empirical distribution function. New inferential methods using sample characteristic functions (Cfs) and moment generating functions (MGFs) seem well-suited to mixtures. since these transforms often take simple form/ This paper reports a simulation study of the properties of estimators and tests of fit based on CFs, MGFs, and sample moments when applied to three specific families of thick tailed mixture distributios.