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MATHEMATICS
On generalizations of the optimal choice problem
I. V. Belkov St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Abstract:
The article is dedicated to some generalizations of the classical optimal choice problem (the fastidious bride problem, the secretary problem). Let there be a sequence of n identically distributed random variables on the interval $[0, 1]$. Getting consistently observed values of these variables, we should stop at some moment on one of them, accepting it as the initial point for counting upper or lower record values. In the optimal choice problem and its generalizations, it is needed to make the correct choice of the initial point of counting records, in order to guess the place of the last record (the classical optimal choice problem) or to maximize the expected sum of upper and/or lower record values or the expected total number of upper and/or lower records, obtained by this procedure. A review of results on the uniform distribution of the random variables and some new results concerning the exponential distribution are presented.
Keywords:
record moments, record values, sums of record values, mean number of records, uniform distribution, exponential distribution, optimal choice problem.
Received: 28.08.2020 Revised: 15.09.2020 Accepted: 17.09.2020
Citation:
I. V. Belkov, “On generalizations of the optimal choice problem”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:1 (2021), 29–36; Vestn. St. Petersbg. Univ., Math., 8:3 (2021), 22–27
Linking options:
https://www.mathnet.ru/eng/vspua129 https://www.mathnet.ru/eng/vspua/v8/i1/p29
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Abstract page: | 31 | Full-text PDF : | 29 |
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