I'm modeling a process made up of several independent, consecutive steps. I'm using a Gamma distribution for the duration of each step, so the total duration is the sum of several independent Gamma variables. Is there a closed form for the distribution of the total duration, as a function of the various Gamma parameters?
I'd actually like to use a truncated Gamma (i.e., limited to a maximum and minimum value) for the steps. Does that make the distribution of the total duration too messy?
If there is no closed form, is there a reasonable approximation that anyone can suggest? I'm doing this in Visual Basic (Excel was way too slow) so I am quite flexible about what kind of algorithm to implement.
Thanks for your help!
Dan Goddard
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