G. Christoph, V. V. Ulyanov, “On accuracy of approximations for standardized chi-squared distributions by Edgeworth–Chebyshev expansions”, Inform. Primen., 2011, Volume 5, Issue 1,Pages <nobr>25

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

G. Christoph^a, V. V. Ulyanov^b

^a Institute for Mathematical Stochastics, Faculty of Mathematics, University of Magdeburg, Magdeburg, Germany
^b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: 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.

Keywords: asymptotic expansions; error bounds; chi-squared distribution.