On accuracy of approximations for standardized chi-squared distributions by Edgeworth–Chebyshev expansions

Astandardized chi-squared randomvariable Vn with n degrees of freedomis consideredwith Edgeworth–Chebyshev expansions, the computable error bounds of orders $O(n^{-1/2})$, $O(n^{-1})$ and $O(n^{-3/2})$ for approximations of Vn have been obtained. The results are useful in applications, in particular, in analysis of statistics ratio of probability features.