Gamma Distribution Question

I work at an organ transplant center. When I made a graph of the organs
harvested per month, it follows a Gamma distribution better than a normal
distribution.

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

Histogram

http://www.mixedasians.com/member_pics/haplotype_1187586650.gif

QQ plot

http://www.mixedasians.com/member_pics/haplotype_1187586657.gif


Thanks

.

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