Extreme order statistics with cost of sampling

Abstract

Let X1, X2, …, Xn, … be mutually independent with common CDF F and, for each m, n, let Xm:n be the mth largest among the first n. We consider max1≤n<∞ (X1:n – cn) and the ‘optimal stopping rule' N which maximizes where all l and In particular, we consider and All of these are considered for c ϵ (0,∞) as well as asymptotically as c → 0+.