An Application of the Residue Calculus: The Distribution of the Sum of Non-Homogeneous Gamma Variates
Robert C. Hagwood
The probability density function for the sum of gamma variates with different shape parameters is found, using the inversion formula and the calculus of residues. This derivation seems more elegant than previous methods to derive the probability density function. Furthermore, the computation of the density is straight forward, especially in any symbolic language.
An Application of the Residue Calculus: The Distribution of the Sum of Non-Homogeneous Gamma Variates, The American Statistician, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=51284
(Accessed November 30, 2023)