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An extension of Mineka’s coupling inequality. (English) Zbl 1189.60095
Summary: We propose a refinement of Mineka’s coupling inequality that gives a better upper bound for \(d_{TV}({\mathcal L}(W),{\mathcal L}(W+1))\), where \(W\) is a sum of \(n\) independent integer valued random variables, in the case when \({\mathbf{var}}\, W\gg n\).

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