What would it be when the sum of two independent gamma random variables with different parameters.?eg: X~Gamma(a,b) and Y~Gamma(c,d) ,Then X+Y?

25 July 2022 1 7K Report

The sum of two independent random variables is also a gamma random variable. What would it be when the sum of two independent gamma random variables with different parameters. eg: X~Gamma(a,b) and Y~Gamma(c,d) ,Then the distribution function of X+Y?

Steftcho P. Dokov

Looks like that (2.9) and (2.10) in

https://www.ism.ac.jp/editsec/aism/pdf/037_3_0541.pdf

yield the pdf and cdf (that you are looking for), respectively.

or: (same one is seen here)

https://link.springer.com/article/10.1007/BF02481123?noAccess=true

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