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Binomial approximation for dependent indicators. (English) Zbl 0856.60026
Summary: A binomial approximation theorem for dependent indicators using Stein’s method and coupling is proved. The approximating binomial distribution \(B(n', p')\) is chosen in such a way that its first moment is equal to that of \(W\) and its variance is asymptotically equal to that of \(W\) as \(n'\) tends to infinity where \(W\) is the sum of independent indicators and \(p'\) is bounded away from 1. Three examples, one of which concerns two different approximations for the hypergeometric distribution, are given to illustrate applications of the theorem obtained.

60E99 Distribution theory
60F05 Central limit and other weak theorems