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Zbl 1189.60095
Posfai, Anna
An extension of Mineka's coupling inequality. (English)
[J] Electron. Commun. Probab. 14, 464-473, electronic only (2009). ISSN 1083-589X/e

Summary: We propose a refinement of Mineka's coupling inequality that gives a better upper bound for $d_{TV}({\cal L}(W),{\cal L}(W+1))$, where $W$ is a sum of $n$ independent integer valued random variables, in the case when ${\bold{var}}\, W\gg n$.

MSC 2000:: *60G50 Sums of independent random variables
62E17 Approximations to statistical distributions (nonasymptotic)

Keywords: Mineka coupling; translated compound Poisson approximation; total variation distance; coupon collecting

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