On the Distribution of the Weighted Sum of Chi-Squared Variables

Ayse Unsal; Raymond Knopp

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arXiv · 2203.11940

On the Distribution of the Weighted Sum of Chi-Squared Variables

Ayse Unsal·Raymond Knopp

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Abstract

This paper presents the probability distribution function (p.d.f.) and cumulative distribution function (c.d.f.) of the weighted sum of central independent chi-squared random variables with non-zero weighs based on a method using moment generating functions. To obtain the p.d.f. and c.d.f. of such a function, we first derive the moment generating function of this weighted sum using the partial fractions decomposition or the residue method. The results cover the sum of two and three weighted chi-squared random variables, which can easily be adapted to more general cases.

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Ayse Unsal, Raymond Knopp. 2021-09-14. On the Distribution of the Weighted Sum of Chi-Squared Variables. https://arxiv.org/abs/2203.11940

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