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Comment: Trashed by: elnaz; Original Page Title: Normal approximation to the Poisson distribution; Scroll Page Title: Normal approximation to the Poisson distribution; Scroll Page Id: AC1F2FA0015F82D814F933791CE95800;Original Scroll Version: Currently Published;

 

 

The Poisson(lt) distribution describes the possible number of events that may occur in an exposure of t units, where the average number of events per unit of exposure is l. A Poisson(lt) distribution is thus the sum of t independent Poisson(l) distributions. We might intuitively guess then that if lt is sufficiently large, a Poisson(lt) distribution will start to look like a Normal distribution, because of Central Limit Theorem, as is indeed the case. A Poisson(1) distribution (see graph below) is quite skewed, so we would expect to need to add together some 20 or so before the sum would look approximately Normal.

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