Letter to the Editor—An Optimal Stopping Rule

Suppose the random variables X₁, X₂, …, all from the same population, are observed sequentially. After the nth observation, the experimenter can stop and receive the net payoff of c₁ [max(x₁, x₂, …, x_n)] − nc₂, where c₁ is the unit value of the maximum and c₂ is the sampling cost. In this paper a rule is given to determine if the experimenter should stop in the nth observation or if he should continue until the (n + 1)st observation, at which time he is faced with this decision all over again.