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arXiv · 2412.12937

An integral over $(0,\pi)$ for the distribution function of a sum of independent gamma random variables and for quadratic forms of Gaussian variables

Thomas Royen
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Abstract

An integral over the interval $(0,\pi)$ is given for the cumulative distribution function of a sum of independent gamma random variables with different scale and shape parameters. The cumulative distribution function of a positive definite quadratic form is obtained as a special case with identical shape parameters $\alpha = 1/2$.

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Thomas Royen. 2024-12-17. An integral over $(0,\pi)$ for the distribution function of a sum of independent gamma random variables and for quadratic forms of Gaussian variables. https://arxiv.org/abs/2412.12937

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