The secretary problem for selecting one item so as to minimize its expected rank, based on observing the relative ranks only, is revisited. A simple suboptimal rule, which performs almost as well as the optimal rule, is given. The rule stops with the smallest i such that Ri = ic/(n + 1 - i) for...

The present paper studies the limiting behavior of the average score of a sequentially selected group of items or individuals, the underlying distribution of which, F, belongs to the Gumbel domain of attraction of extreme value distribution. This class contains the Normal, log Normal, Gamma,...

A version of a secretary problem is considered: Let X_j, j = 1,...,n be i.i.d. random variables. Like in the classical secretary problem the optimal stopper only observes Y_j = 1, if X_j is a (relative) record, and Y_j = 0, otherwise. The actual X_j-values are not revealed. The goal is to maximize...

Let X_i be nonnegative independent random variables with finite expectations and X^*_n = max {X_1, ..., X_n}. The value EX^*_n is what can be obtained by a ``prophet". A ``mortal" on the other hand, may use k = 1 stopping rules t_1, ..., t_k yielding a return E[max_{i=1, ..., k} X_{t_i}]. For n...

In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider situations where the available information is the rank of...

Asymptotic results for the problem of optimal two choice stopping on an n element long i.i.d. sequence X<SUB>n</SUB>, . . . ,X<SUB>1</SUB> have previously been obtained for two of the three domains of attraction. An asymptotic result is proved for the exponential distribution, a representative from the remaining,...</sub></sub>

Let Xn, . . . ,X1 be i.i.d. random variables with distribution function F. A statistician, knowing F, observes the X values sequentially and is given two chances to choose X’s using stopping rules. The statistician’s goal is to stop at a value of X as small as possible. Let V^2 equal the...