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Optical Memory and Neural Networks

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01-03-2023

Density Function of Weighted Sum of Chi-Square Variables with Trigonometric Weights

Authors: V. I. Egorov, B. V. Kryzhanovsky

Published in: Optical Memory and Neural Networks | Issue 1/2023

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Abstract

We have investigated a weighted chi-square distribution of the variable ξ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles \({{\varphi }_{k}} = {{2\pi k} \mathord{\left/ {\vphantom {{2\pi k} N}} \right. \kern-0em} N},\) where \(k \in \left\{ {0,1,...,N - 1} \right\}\) and N is the number of the freedom degrees. We have found the exact expression for the density function of this distribution and its approximation for large N. The distribution is compared with the Gaussian distribution.

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Title: Density Function of Weighted Sum of Chi-Square Variables with Trigonometric Weights
Authors: V. I. Egorov
B. V. Kryzhanovsky
Publication date: 01-03-2023
Publisher: Pleiades Publishing
Published in: Optical Memory and Neural Networks / Issue 1/2023
Print ISSN: 1060-992X
Electronic ISSN: 1934-7898
DOI: https://doi.org/10.3103/S1060992X23010071

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