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The Gamma Distribution

​
parameter α
1.825
parameter β
1.945
mean:
αβ
=
3.550
variance:
α
2
β
=
6.904
moment generating function:
-α
(1-βt)
=
1
1.825
(1-(1.945+0.)t)
The waiting time to observe the occurrence of
α
events in a Poisson process with intensity
1/β
is a random variable that follows the Gamma distribution with parameters
α
and
β
(both of which must be positive). The red vertical segment marks the mean of the distribution.
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