Characterization of the monotone case for a best choice problem with a random number of objects
The author considers the following full-information best choice problem with a random number of objects. When the number of objects \(N\) is a random variable, a sequence of i.i.d. random variables \(X_1,X_2,\dots, X_N\) with a known continuous distribution \(F\) is observed sequentially. The objective is to maximize the probability of choosing the largest. Such a problem was investigated by the author [Stochastic Processes Appl. 24, 293-307 (1987; Zbl 0623.60059)], in which the monotone case occurs for a class of distributions of \(N\), \(N\) is characterized by the number of sign changes of certain sequence, and the optimal stopping time is given. The author gives a more convenient way of checking whether the distribution of \(N\) gives the monotone case and shows that the new characterization forms a class of distributions which is a subclass of IFR distributions.
scientific article; zbMATH DE number 1796703