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An Application of the Residue Calculus: The Distribution of the Sum of Non-Homogeneous Gamma Variates

Published

Author(s)

Robert C. Hagwood

Abstract

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.
Citation
The American Statistician
Volume
63
Issue
1

Keywords

Gamma variates, residues, inversion formula, distribution

Citation

Hagwood, R. (2009), 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)
Created February 2, 2009, Updated January 27, 2020