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Optimal procedures for a problem of sequential choice of k objects with given ranks Mikhail L. Nikolaev Moscow Open Social University, Mari Branch Karl Marx Str. 140 424006, Yoshkar-Ola, Mari El Russia e-mail: [email protected] George Yu. Sofronov School of Mathematics and Applied Statistics University of Wollongong Wollongong NSW 2522 Australia e-mail: [email protected] Tatyana V. Polushina Mari State University Lenin Square 1 424001, Yoshkar-Ola, Mari El Russia e-mail: [email protected] Abstract A problem of sequential choice of objects with given ranks is considered. We have a known number N of objects numbered 1, 2, . . . , N . It is clear from comparing any two of these objects which one is better, although their actual number still remain unknown. After having known each sequential object, we either accept this object (and then a choice of one object is made), or reject it and continue observation (it is impossible to return to the rejected object). The aim is to find procedure such that the probability of choice of k objects is maximal. In contrast to classical best multiply choice problem we consider case of given (certain) ranks r1 , r1 , . . . , rk , 1 ≤ r1 < . . . < rk ≤ N . The optimal rules τ ∗ for some ranks r1 , . . . , rk are derived. Numerical examples are presented. 1
