Abstract

Let { Xn, n = 1 } be a sequence of independent identically distributed random variables, taking nonnegative integer values. An observation Xn is a tie for the maximum if Xn = max { X1, ..., Xn - 1 }. In this paper, we obtain weak and strong laws of large numbers and central limit theorems for the cumulative number of ties for the maximum among the first n observations. © 2009 Elsevier B.V. All rights reserved.