Letter to the Editor—An Optimal Stopping Rule

Abstract

Suppose the random variables X 1 , X 2 , …, all from the same population, are observed sequentially. After the n th observation, the experimenter can stop and receive the net payoff of c 1 [max( x 1 , x 2 , …, x n )] − nc 2 , where c 1 is the unit value of the maximum and c 2 is the sampling cost. In this paper a rule is given to determine if the experimenter should stop in the n th observation or if he should continue until the ( n + 1)st observation, at which time he is faced with this decision all over again.