Normal approximation to the Gamma distribution


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) » Normal

 

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