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Conditional Evaluations of Sums of Sample Maxima and Records


[ 1 ] Instytut Automatyki i Robotyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.2] Automation, electronics, electrical engineering and space technology

Year of publication


Published in

REVSTAT - Statistical Journal

Journal year: 2023 | Journal volume: vol. 21 | Journal number: no. 2

Article type

scientific article

Publication language


  • sample maximum
  • upper record
  • conditional expectation
  • bound

EN We consider sequences of independent and identically absolutely continuously distributed random variables assuming that they have finite expectation and variance. We determine sharp lower and upper bounds on the expectation of the sum of n first sample maxima and n first upper record values under the condition that the value of the jth (1 ≤ j ≤ n) sample maximum and record value, respectively, are known and equal to a given quantile of the parent distribution. The bounds are expressed in terms of the expectation and standard deviation of the parent distribution. Analogous evaluations are presented for the sum of record values in n observations, when the jth sample maximum is known. The theoretical results are numerically compared.

Date of online publication


Pages (from - to)

235 - 266




License type

CC BY (attribution alone)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

Ministry points / journal


Impact Factor

0.9 [List 2022]

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