Density Function of Weighted Sum of Chi-Square Variables with Trigonometric Weights
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908170324017152 |
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| author | Egorov, Vladislav Kryzhanovsky, Boris |
| author_facet | Egorov, Vladislav Kryzhanovsky, Boris |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_17433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density Function of Weighted Sum of Chi-Square Variables with Trigonometric Weights Egorov, Vladislav Kryzhanovsky, Boris Disordered Systems and Neural Networks Probability 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. |
| title | Density Function of Weighted Sum of Chi-Square Variables with Trigonometric Weights |
| topic | Disordered Systems and Neural Networks Probability |
| url | https://arxiv.org/abs/2412.17433 |