Expansions in Appell polynomials of the convolutions of probability distributions
Articles
Algimantas Bikelis
Vytautas Magnus University, Lithuania
Kazimieras Padvelskis
Vilnius Gediminas Technical University, Lithuania
Published 2013-07-25
https://doi.org/10.15388/NA.18.3.14010
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Keywords

convolution of probability distributions
accompanying law
Appell polynomials
Bergström identity

How to Cite

Bikelis A. and Padvelskis K. (2013) “Expansions in Appell polynomials of the convolutions of probability distributions”, Nonlinear Analysis: Modelling and Control, 18(3), pp. 275-292. doi: 10.15388/NA.18.3.14010.

Abstract

We use the composition method to analyse the convolutions of probability distributions by emploing the Appell polynomials and Bergström identity. Our approximation is based on the probability distributions which have the inverse generalized measure of bounded variation. The idea to use the accompanying probability distribution eλ(F−E),  λ > 0, was first proposed by B.V. Gnedenko [1].

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