title: On one problem of the optimal choice of record values
metadata.name: dc.contributor.author
metadata.value: Belkov, Igor V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Nevzorov, Valery B.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-07-12T19:23:04Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-07-12T19:23:04Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Belkov I.V., Nevzorov V.B. On one problem of the optimal choice of record values. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 2, pp. 179–188.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.201
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/10398
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Let independent random variables X1,X2, . . . have the same continuous distribution function.
  The upper record values X(1) = X1 < X(2) < . . ., generated by this sequence of
  variables, as well as the lower record values x(1) = X1 > x(2) > . . . are considered. It
  is known that in this situation the mean value c(n) of the sum of numbers of the both
  types of records among the first n of X’s is given by equality c(n) = 2(1 + 1
  2 + . . . + 1
  n ),
  n = 1, 2, . . .. The problem considered here is how to obtain the maximal mean value e(n) of
  the considered number of records among the rest of the random variables getting sequentially
  the observed values x1, x2, . . . of X’s and selecting one of them as the initial point. It
  is not possible to come back to rejected elements of the sequence. Some procedures of the
  optimal choice of the initial element Xr are discussed. The corresponding tables for values
  e(n) and differences  (n) = e(n)−c(n) are presented for different values of n. The value of
    = limn→∞  (n) is given also. In some sense the considered problem and presented in the
  paper optimizing procedures are very close to the classical “secretary problem” in which the
  probability to select the last record value in the set of independent identically distributed
  X’s is maximized.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5(63); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: record times
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: record values
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: expected number of records
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: uniform distribution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimal choice problem
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On one problem of the optimal choice of record values
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01-Belkov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/10398/1/01-Belkov.pdf
resources.format: Adobe PDF
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