Domain of Attraction of -stable Distributions under Finite Mixture Models

C.E.G. Otiniano, C.R. Gonçalves

Abstract


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.

References


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DOI: https://doi.org/10.5540/tema.2010.011.01.0069

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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