Summary
The distribution of the sum ofn independent gamma variates with different parameters is expressed as a single gamma-series whose coefficients are computed by simple recursive relations.
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References
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Moschopoulos, P.G. The distribution of the sum of independent gamma random variables. Ann Inst Stat Math 37, 541–544 (1985). https://doi.org/10.1007/BF02481123
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DOI: https://doi.org/10.1007/BF02481123