Density Function of Weighted Sum of Chi-Square Variables with Trigonometric Weights
Abstract
We have investigated a weighted chi-square distribution of the variable which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles φk=2π k/N, where k ∈ \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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.