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A new semigroup technique in Poisson approximation. (English) Zbl 0674.60026

The authors present a new semigroup technique for Poisson approximation of sums of independent Bernoulli random variables. The new method gives a unified approach to derive approximations with respect to various probability metrics. The method is applied to extend their earlier work [Ann. Probab. 14, 663-676 (1986; Zbl 0597.60019), Semigroup Forum 34, 203-224 (1986; Zbl 0606.60034)].
Reviewer: B.L.S.Prakasa Rao

MSC:

60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics
47D03 Groups and semigroups of linear operators
20M30 Representation of semigroups; actions of semigroups on sets
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References:

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