Let X1, X2, … be independent, identically distributed random variables with two-parameter exponential distribution, and suppose that given a sample of size n, the reward is Yn = max{X1, …, Xn} − cn. When the scale parameter is unknown, the optimal fixed sample size n*c for maximizing the expected reward E(Yn) cannot be found. This paper deals with the problem of approximating the optimal fixed sample size expected reward Rn*c through a two-stage procedure and shows that the difference between the expected reward using the proposed procedure and Rn*c vanishes as c approaches zero.
