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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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