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

Abstract

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 α₁ is known, with the intervals constructed with the use of the classical chi-square distribution under the assumption of normality of normalized sums.