A Poisson approximation with applications to the number of maxima in a discrete sample (Q1962159)
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scientific article; zbMATH DE number 1395116
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Poisson approximation with applications to the number of maxima in a discrete sample |
scientific article; zbMATH DE number 1395116 |
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A Poisson approximation with applications to the number of maxima in a discrete sample (English)
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1999
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The joint distribution of the \(k\) largest values of a sample of \(n\) independent and identically distributed random variables is asymptotically the same as that of a Poisson distributed number \(N\), if \(EN= n\) and \(k\) is fixed. The author uses this well known fact to simplify the proofs of some results concerning the number of maxima in discrete samples; see, for example, \textit{B. Eisenberg}, \textit{G. Stengle} and \textit{G. Strang} [Ann. Appl. Probab. 3, No. 3, 731--745 (1993; Zbl 0787.60029)].
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