A semigroup approach to Poisson approximation with respect to the point metric (Q1903178)
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scientific article; zbMATH DE number 820299
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A semigroup approach to Poisson approximation with respect to the point metric |
scientific article; zbMATH DE number 820299 |
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A semigroup approach to Poisson approximation with respect to the point metric (English)
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26 November 1995
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Let \(X_1, \ldots, X_n\) be independent Bernoulli random variables. The article compares the distribution of \(S_n = \sum^n_{j = 1} X_j\) with suitable Poisson distributions, using as measure of discrepancy the largest difference between two point probabilities. Sharp asymptotic formulae for the discrepancy are derived, using the operator approach of \textit{P. Deheuvels} and \textit{D. Pfeifer} [Ann. Probab. 14, 663-676 (1986; Zbl 0597.60019)].
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sharp asymptotic formulae
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independent Bernoulli random variables
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Poisson distributions
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measure of discrepancy
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