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An Analog of the Chi-Square Distribution for Normalized Sums with Small Number of Summands

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In the present paper we obtain approximations to the distribution of a sum of squared normalized variables with small number of summands, and provide an estimate of approximation accuracy. We compare confidence intervals for the unknown parameter σ constructed with the use of the obtained approximations when α 1 is known, with the intervals constructed with the use of the classical chi-square distribution under the assumption of normality of normalized sums.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Perm, Russia

    M. V. Radionova

  2. Perm State National Research University, Perm, Russia

    P. N. Sapozhnikov

Authors
  1. M. V. Radionova
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  2. P. N. Sapozhnikov
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Corresponding author

Correspondence to M. V. Radionova.

Additional information

Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 19, pp. 135–148, 2006

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Radionova, M.V., Sapozhnikov, P.N. An Analog of the Chi-Square Distribution for Normalized Sums with Small Number of Summands. J Math Sci 220, 724–733 (2017). https://doi.org/10.1007/s10958-016-3216-0

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  • DOI: https://doi.org/10.1007/s10958-016-3216-0

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