Discussiones Mathematicae Probability and Statistics 25(2) (2005) 161-179

Approximation by Poisson law

Aldona Aleskeviciene

Institute of Mathematics and Informatics
Akademijos 4, Vilnius 2600, Lithuania

e-mail: stat@ktl.mii.lt

Vytautas Statulevicius

Institute of Mathematics and Informatics
Akademijos 4, Vilnius 2600, Lithuania

Abstract

We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.

Keywords: Poisson distribution, compound Poisson distribution, asymptotic expansions, large deviations, cumulants.

2000 Mathematics Subject Classification: 60F(10).

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Received 15 March 2004
Revised 16 May 2005