On the Distribution of the Weighted Sum of Chi-Squared Variables
Information Theory
2022-03-24 v1 math.IT
Probability
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.
Keywords
Cite
@article{arxiv.2203.11940,
title = {On the Distribution of the Weighted Sum of Chi-Squared Variables},
author = {Ayse Unsal and Raymond Knopp},
journal= {arXiv preprint arXiv:2203.11940},
year = {2022}
}