Domain of Attraction of -stable Distributions under Finite Mixture Models - Otiniano, C.E.G.; Gonçalves, C.R. (Trends in Computational and Applied Mathematics, 2010)
In this work, we study the asymptotic distribution of the normalized sum of independent, identically distributed random variables under the finite mixture models. In the Theorem we give necessary conditions for a distribution function of a mixed population with k components to belong to the domain of attraction of an α-stable distribution, by assuming that each component of the mixture also pertains to the domain of attraction of an α-stable distribution. Examples are given to illustrate the result.