The distributions of interrecord fillings

Oleg P. Orlov; Nikolay Yu. Pasynkov

doi:10.1515/dma-2016-0019

Article

The distributions of interrecord fillings

Oleg P. Orlov and Nikolay Yu. Pasynkov

Published/Copyright: August 20, 2016

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From the journal Discrete Mathematics and Applications Volume 26 Issue 4

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 (i⩾1,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,1⩽j⩽i⩽n, are derived, limit theorems for the distributions of

αij for i − j → ∞ are proved.

Key Words: independent random variables; records; record moments; explicit formulas for distributions; limit theorems

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

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https://doi.org/10.1515/dma-2016-0019

Keywords for this article

independent random variables; records; record moments; explicit formulas for distributions; limit theorems

Articles in the same Issue

Frontmatter
Research Article
Characterization of almost perfect nonlinear functions in terms of subfunctions
Research Article
Estimates for distribution of the minimal distance of a random linear code
Research Article
The distributions of interrecord fillings
Research Article
Galois theory for clones and superclones
Research Article
Overgroups of order 2ⁿ additive regular groups of a residue ring and of a vector space