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

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 approximat...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2017-02, Vol.220 (6), p.724-733
Main Authors: Radionova, M. V., Sapozhnikov, P. N.
Format: Article
Language:English
Subjects:
Chi-square test
Confidence intervals
Mathematics
Mathematics and Statistics
Normality
Sums
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-016-3216-0