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Journal of Mathematical Sciences

, Volume 220, Issue 6, pp 724–733 | Cite as

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

  • M. V. RadionovaEmail author
  • P. N. Sapozhnikov
Article
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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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsPermRussia
  2. 2.Perm State National Research UniversityPermRussia

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