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Convergence of the sequence of the Pearson statistics values to the normalized square of the Bessel process

Authors
  • Zubkov, Andrey M.
  • Savelov, Maksim P.
Type
Published Article
Journal
Discrete Mathematics and Applications
Publisher
De Gruyter
Publication Date
Dec 07, 2017
Volume
27
Issue
6
Pages
405–411
Identifiers
DOI: 10.1515/dma-2017-0041
Source
De Gruyter
Keywords
License
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Abstract

It is shown that, with suitable time change, the finite-dimensional distributions of the process formed by successive values of the Pearson statistics for an expanding sample converge to finite-dimensional distributions of the stationary random process, namely, the normalized square of the Bessel process. The results obtained earlier on the limit joint distributions of the Pearson statistics are used to derive explicit formulas for the density of joint distributions of the Bessel process.

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