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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 466, Pages 30–37
(Mi znsl6538)
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On one problem of the optimal choice of record values
I. V. Bel'kov, V. B. Nevzorov St. Petersburg State University, St. Petersburg, Russia
Abstract:
Independent random variables $X_1,X_2,\dots, X_n$ having $\mathrm U([0,1])$-uniform distribution and the upper record values in this set are considered. We study the problem how to maximize (taking into account some consecutively observed values $x_1,x_2,\dots,x_k$ of these $X$-s) the expectation of sums of records in this sequence under the optimal choice of the corresponding variable $X_k$ (instead of $X_1$) as the initial record value.
Key words and phrases:
record times, record values, sums of record values, expected number of records, uniform distribution, optimal choice problem.
Received: 12.10.2017
Citation:
I. V. Bel'kov, V. B. Nevzorov, “On one problem of the optimal choice of record values”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 30–37
Linking options:
https://www.mathnet.ru/eng/znsl6538 https://www.mathnet.ru/eng/znsl/v466/p30
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Abstract page: | 184 | Full-text PDF : | 71 | References: | 26 |
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