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Short Communications

On the decomposition of lattice distributions into convolutions of Poisson signed measures

D. N. Karymov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: This work provides some results on the convolutions of a special kind of signed measure known as the Poisson signed measure. We show a simple way of obtaining asymptotic decompositions into convolutions of Poisson signed measure that is appropriate for a broad range of lattice distributions. The work demonstrates the analogy between such decompositions and the classic Gram–Charlier decompositions of type $A$ and $B$, and the Edgeworth-Cramer series.

Keywords: Poisson signed measure, convolutions of Poisson signed measure, asymptotic decompositions, lattice random variables.

Received: 16.04.2004

DOI: 10.4213/tvp209

 English version: Theory of Probability and its Applications, 2005, 49:3, 545–552

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