Approximation of CDF of Non-Central Chi-Square Distribution by Mean-Value Theorems for Integrals

Árpád Baricz, Dragana Jankov Maširević and Tibor K. Pogány
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Árpád Baricz: Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania
Dragana Jankov Maširević: Department of Mathematics, University of Osijek, Trg Lj. Gaja 6, 31000 Osijek, Croatia
Tibor K. Pogány: Institute of Applied Mathematics, Óbuda University, Bécsi út 96/b, 1034 Budapest, Hungary

Mathematics, 2021, vol. 9, issue 2, 1-12

Abstract: The cumulative distribution function of the non-central chi-square distribution ? n ? 2 ( ? ) of n degrees of freedom possesses an integral representation. Here we rewrite this integral in terms of a lower incomplete gamma function applying two of the second mean-value theorems for definite integrals, which are of Bonnet type and Okamura’s variant of the du Bois–Reymond theorem. Related results are exposed concerning the small argument cases in cumulative distribution function (CDF) and their asymptotic behavior near the origin.

Keywords: non-central ? 2 distribution; second mean-value theorem for definite integrals; modified Bessel function of the first kind; Marcum Q –function; lower incomplete gamma function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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