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arXiv · 2412.17433

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

Vladislav Egorov·Boris Kryzhanovsky
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Abstract

We have investigated a weighted chi-square distribution of the variable $\xi$ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles $\phi_k=2\pi k/N$, where $k \in \{0,1,...,N-1\}$ 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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Vladislav Egorov, Boris Kryzhanovsky. 2024-12-23. Density Function of Weighted Sum of Chi-Square Variables with Trigonometric Weights. https://doi.org/10.3103/s1060992x23010071

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