[R] About poisson distribution fitting and testing

Rolf Turner rolf at math.unb.ca
Thu Apr 20 01:26:13 CEST 2006

(a) Surely to gumdrops, fitting a ***Poisson*** distribution
is as trivial as it gets.  There's one parameter to estimate;
lambda.hat <-  x.bar <- mean(x).

(b) If the mean is 6 and the variance is 11, the data are VERY
unlikely to be Poisson.  If X is Poisson, var(X) = E(X).  No
indication of the sample size was given, but let's take a sample size
of 30 for the purposes of illustration.  In this case the probability
of getting a variance of 11 from a Poisson distribution with
(population) mean equal to 6 is (approximately, by simulation) 0.004.

(c) A chi-squared goodness of fit test will also (almost surely!)
tell you that the data are not Poisson.


				Rolf Turner
				rolf at math.unb.ca

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