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

2024/12/17 by Royen, Thomas
#60G50 #62E15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2412.12937

Abstract

An integral over the interval (0,π) 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 α= 1/2.

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