Two-stage procedures for approximating the expected reward: The negative exponential case

Abstract.

Let X ₁, X ₂, … be i.i.d. random variables with two-parameter exponential distribution, and suppose that given a sample of size n, the reward is Y _n=max {X ₁, …, X _n}−c n. When the scale parameter is unknown, the optimal fixed sample size n _c ^* for maximizing the expected reward E (Y _n) cannot be found. This paper deals with the problem of approximating the optimal fixed sample size expected reward R _nc* through a two-stage procedure and shows that the difference between the expected reward using the proposed procedure and R _nc* vanishes as c approaches zero.