On the multiplicity of the maximum in a discrete random sample (Q1429104)

Let \(X_1,\dots,X_n\) be independent and identically distributed integer valued random variables. Let \(M_n=\max\{ X_1,\dots\}\) and let \(W_n\) be the number of \(i\)'s, \(1\leq i\leq n\), such that \(X_i=M_n\). The aim of this paper is to investigate the asymptotic behavior of the distribution of \(W_n\) as \(n\to \infty\). The main tool of the authors' approach is based on the Sukhatme-Renyi representation of exponential order statistics, which gives, as they think, new insights into this problem.