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The distributions of interrecord fillings

  • Oleg P. Orlov EMAIL logo und Nikolay Yu. Pasynkov
Veröffentlicht/Copyright: 20. August 2016
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Abstract

In a sequence of independent positive random variables with the same continuous distribution function a monotonic subsequence of record values is chosen. A corresponding sequence of record times divides the initial sequence into interrecord intervals. Let

αij(i1,j=1,,i) be the number of random variables in the interval between i-th and (i + 1)-th record moments with values between (j − 1)-th and j-th records. Explicit formulas for the joint distributions of the random variables
αij,1jin
, are derived, limit theorems for the distributions of
αij
for ij → ∞ are proved.


Originally published in Diskretnaya Matematika (2015) 27, №3, 56-73 (in Russian).


Acknowledgement

The authors are grateful to their science supervisor, Vasiliy Vasilievich Kozlov, for the problem statement and constant support and also to Andrey Michailovich Zubkov for discussion of the problem and important comments on the paper.

References

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Received: 2015-1-12
Published Online: 2016-8-20
Published in Print: 2016-8-1

2016 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 27.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/dma-2016-0019/html
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