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Teor. Veroyatnost. i Primenen., 1995, Volume 40, Issue 4, Pages 925–928 (Mi tvp3688)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Asymptotics of the $k$th record times

A. L. Yakymiv

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Let $\eta_{0,n}\le\eta_{1,n}\le…\le\eta_{n,n}$ be the set of ordered statistics constructed by a sequence of independent identically distributed random variables $\eta_0,\eta_1,…,\eta_n$ and let $\nu^{(k)}(0)=k-1$,
$$ \nu^{(k)}(n+1)=\min\{j>\nu^{(k)}(n):\eta_j>\eta_{j-k,j-1}\}, \qquad n=0,1,2,…, $$
be the $k$th record times. For fixed $k$ and $n$, the asymptotic behavior of the probability $\mathbf P\{\nu^{(k)}(n)>t\}$ is studied as $t\to\infty$.

Keywords: the set of ordered statistics, record times, kth record times.

Full text: PDF file (188 kB)

English version:
Theory of Probability and its Applications, 1995, 40:4, 794–797

Bibliographic databases:

Received: 09.02.1993

Citation: A. L. Yakymiv, “Asymptotics of the $k$th record times”, Teor. Veroyatnost. i Primenen., 40:4 (1995), 925–928; Theory Probab. Appl., 40:4 (1995), 794–797

Citation in format AMSBIB
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\by A.~L.~Yakymiv
\paper Asymptotics of the $k$th record times
\jour Teor. Veroyatnost. i Primenen.
\yr 1995
\vol 40
\issue 4
\pages 925--928
\mathnet{http://mi.mathnet.ru/tvp3688}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1405161}
\zmath{https://zbmath.org/?q=an:0859.60049}
\transl
\jour Theory Probab. Appl.
\yr 1995
\vol 40
\issue 4
\pages 794--797
\crossref{https://doi.org/10.1137/1140094}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WD22100024}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ahsanullah M., “Characterizations of Univariate Continuous Distributions”, Characterizations of Univariate Continuous Distributions, Atlantis Studies in Probability and Statistics, 7, Atlantis Press, 2017, 1–125  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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