title: On the second record derivative of a sequence of exponential random variables
metadata.name: dc.contributor.author
metadata.value: Nevzorov, Valery B.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Stepanov, Alexei V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T12:36:33Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T12:36:33Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Nevzorov V.B., Stepanov A.V. On the second record derivative of a sequence of exponential random variables. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 69–76.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.107
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17329
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Let Zi (i   1) be a sequence of independent and identically distributed random variables
  with standard exponential distribution H and Z(n) (n   1) be the corresponding
  sequence of exponential records associated with Zi (i   1). Let us call the sequence
  Z(n) (n   1) the first “record derivative” of the sequence Zi (i   1). It is known that ν1 = Z(1), ν2 = Z(2) − Z(1), . . . are independent variables with distribution
  H. Let T (n) (n   1) be record times obtained from the sequence ν1, ν2, . . . and
  Y (n) = Z(T (n)),W(n) = Y (n) − Y (n − 1) (n   1). Let us call the sequence Y (n) (n   1)
  (the main objective of the research of the present paper) the second “record derivative” of
  the sequence Zi (i   1). In the present paper, we find the distributions of T (n), Y (n),W(n)
  and study the Laplace transform of Y (n). A limit result for the sequence Y (n) (n   1) is
  obtained in the paper. We also propose some methods of generation of T (n) and Y (n).
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work of V.B.Nevzorov is supported by Russian Foundation for Basic Research (grant N18-
  01-00393).
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 7 (65); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: record values
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: exponential distribution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: limit results
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: methods of record generation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the second record derivative of a sequence of exponential random variables
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 69-76.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17329/1/69-76.pdf
resources.format: Adobe PDF
resources.size: 305,89 kB