engleski

Approximation of CDF of non-central chi-square distribution by mean-value theorems for integrals

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

Non-central χ² distribution ; Second mean-value theorem for definite integrals ; Modified Bessel function of the first kind ; Marcum Q-function ; Lower incomplete gamma function

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