A Poisson approximation with applications to the number of maxima in a discrete sample
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)].
scientific article; zbMATH DE number 1395116