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Infinitely divisible approximations for discrete nonlattice variables

Part of: Limit theorems Distribution theory - Probability

Published online by Cambridge University Press:  01 July 2016

V. Čekanavičius
V. Čekanavičius*
Affiliation:
Vilnius University
*
∗ Postal address: Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Email address: vydas.cekanavicius@maf.vu.lt
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Abstract

Sums of independent random variables concentrated on discrete, not necessarily lattice, set of points are approximated by infinitely divisible distributions and signed compound Poisson measures. A version of Kolmogorov's first uniform theorem is proved. Second-order asymptotic expansions are constructed for distributions with pseudo-lattice supports.

Keywords

Compound Poisson distributionKolmogorov's uniform theoremuniform distancetotal variationdiscrete nonlattice random variable

MSC classification

Primary: 60F99: None of the above, but in this section
Secondary: 60F05: Central limit and other weak theorems 60E05: Distributions
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 982 - 1006
Copyright
Copyright © Applied Probability Trust 2003 

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