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 Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 30–37 (Mi znsl6538)

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 $X_1,X_2,…, X_n$ 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 $x_1,x_2,…,x_k$ 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.

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Document Type: Article
UDC: 519.2

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

Citation in format AMSBIB
\Bibitem{BelNev17} \by I.~V.~Bel'kov, V.~B.~Nevzorov \paper On one problem of the optimal choice of record values \inbook Probability and statistics. Part~26 \serial Zap. Nauchn. Sem. POMI \yr 2017 \vol 466 \pages 30--37 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6538}