Permanent URL to this publication: http://dx.doi.org/10.5167/uzh21917
Barbour, A D; Cekanavicius, V (2002). Total variation asymptotics for sums of independent integer random variables. The Annals of Probability, 30(2):509545.

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Abstract
Let $W_n := \sum_{j=1}^n Z_j$ be a sum of independent integervalued random variables. In this paper, we derive an asymptotic expansion for the probability $\mathbb{P}[W_n \in A]$ of an arbitrary subset $A \in \mathbb{Z}$. Our approximation improves upon the classical expansions by including an explicit, uniform error estimate, involving only easily computable properties of the distributions of the $Z_j:$ an appropriate number of moments and the total variation distance $d_{\mathrm{TV}}(\mathscr{L}(Z_j), \mathscr{L}(Z_j + 1))$. The proofs are based on Stein’s method for signed compound Poisson approximation.
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Additional indexing
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
Dewey Decimal Classification:  510 Mathematics 
Uncontrolled Keywords:  compound Poisson; Stein's method; total variation distance; Kolmogorov's problem 
Language:  English 
Date:  2002 
Deposited On:  07 Apr 2010 10:12 
Last Modified:  05 Apr 2016 13:25 
Publisher:  Institute of Mathematical Statistics 
ISSN:  00911798 
Publisher DOI:  10.1214/aop/1023481001 
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