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The Gamma(a,
b)
distribution returns the "time" we will have to wait before
observing a
independent Poisson
events, where one has to wait on average b
units of "time" between each event. The "time" to
wait before a single event occurs is a Gamma(1, b)
= Expon(b)
distribution, with mean b and
standard deviation b too. The Gamma(a,
b)
is thus the sum of a
independent Expon(b)
distributions, so Central
Limit Theorem tells us for sufficiently large a
(>30, for example), we can make the approximation:
Gamma(a,
b)
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