[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.
cheers,
Rolf Turner
rolf at math.unb.ca
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