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Density Function of Weighted Sum of Chi-Square Variables with Trigonometric Weights
Vladislav Egorov, Boris Kryzhanovsky · 2024-12-23 · via math.PR updates on arXiv.org

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 $φ_k=2πk/N$, 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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