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Matematicheskie Zametki, 2008, Volume 83, Issue 6, Pages 899–911
DOI: https://doi.org/10.4213/mzm4050
(Mi mzm4050)
 

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

Limit Distributions of the $\chi^2$ Statistic of K. Pearson in a Sequence of Independent Trials

B. I. Selivanov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (486 kB) Citations (1)
References:
Abstract: We study the $\chi^2$ statistic of K. Pearson in a sequence of independent and, generally, inhomogeneous trials with a fixed number of outcomes. It is assumed that the probabilities of occurrence of outcomes of the trials satisfy certain conditions. This problem statement embraces familiar results for the $\chi^2$ statistic in the case of multinomial trials. We obtain explicit expressions and estimates for the expectation and the variance of the $\chi^2$ statistic. For the $\chi^2$ statistic centered and normalized in a suitable way, we find limit distributions (the normal one, the distribution of the sum of the squares of normal random variables and, in particular, the $\chi^2$ distribution). Conditions for the convergence to the corresponding limit distributions are given.
Keywords: $\chi^2$ statistic of K. Pearson, $\chi^2$ distribution, normal distribution, goodness-of-fit test, multinomial trials, (in)homogenous trials, asymptotically normal random variable.
Received: 23.03.2006
Revised: 20.11.2006
English version:
Mathematical Notes, 2008, Volume 83, Issue 6, Pages 821–832
DOI: https://doi.org/10.1134/S0001434608050271
Bibliographic databases:
Document Type: Article
UDC: 519.24
Language: Russian
Citation: B. I. Selivanov, “Limit Distributions of the $\chi^2$ Statistic of K. Pearson in a Sequence of Independent Trials”, Mat. Zametki, 83:6 (2008), 899–911; Math. Notes, 83:6 (2008), 821–832
Citation in format AMSBIB
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\paper Limit Distributions of the $\chi^2$ Statistic of K.~Pearson in a Sequence of Independent Trials
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\issue 6
\pages 899--911
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\jour Math. Notes
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  • https://www.mathnet.ru/eng/mzm4050
  • https://doi.org/10.4213/mzm4050
  • https://www.mathnet.ru/eng/mzm/v83/i6/p899
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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