Re: Gamma Distribution Question

All the texbooks and Google searches I've looked through only give the properties of Gamma distributions, and that it was invented by Pearson/Weatherburn. But what is the causative mechanism behind a Gamma distribution? I've seen it used to model the speed of gas molecules or rain accumulation. What relation does it have to Poisson processes?

The sum of k independent identically distrubuted exponential random variables has a gamma distribution. Thus, the waiting time to the kth arrival in a Poisson process has a gamma distribution.

The waiting time between organ harvests does follow an exponential distribution almost perfectly.

In that case, you should be considering the Poisson distribution for the counts.
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