We consider a sequential rule, where an item is chosen into the group, such as a university faculty member, only if his score is better than the average score of those already belonging to the group. We study four variables: The average score of the members of the group after k items have been...

Let X_n,…,X₁ be i.i.d. random variables with distribution function F and finite expectation. 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 select a value of X as large as possible. Let V_n²...

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...

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...