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Compound Poisson approximations for sums of discrete nonlattice variables

Part of: Distribution theory - Probability Limit theorems

Published online by Cambridge University Press:  01 July 2016

V. Čekanavičius  and
Y. H. Wang
V. Čekanavičius*
Affiliation:
Vilnius University
Y. H. Wang*
Affiliation:
Tunghai University
*
∗ Postal address: Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Email address: [email protected]
∗∗ Postal address: Department of Statistics, Tunghai University, No. 181, Section 3, Taichung-Kan Road, Taichung, Taiwan 407-04, Republic of China.
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Abstract

Sums of independent random variables concentrated on the same finite discrete, not necessarily lattice, set of points are approximated by compound Poisson distributions and signed compound Poisson measures. Such approximations can be more accurate than the normal distribution. Short asymptotic expansions are constructed.

Keywords

Compound Poisson distributionsigned compound Poisson measureuniform distance

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 1 , March 2003 , pp. 228 - 250
Copyright
Copyright © Applied Probability Trust 2003 

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