Re: Poisson question

In article <1139819280.946242.181400@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
C6L1V@xxxxxxx <C6L1V@xxxxxxx> wrote:

For the exact Poisson distribution, the variance equals the mean, but
for a finite _sample_ from the Poisson distribution, there is no reason
why this should be true. However, your question *does* raise an
interesting point: for a Poisson distribution, we seem to have two
different unbiased estimators of variance. The first is just the mean
itself, which is unbiased as a measure of the mean and hence also of
the variance. The second one is the usual sample variance, which is
known to be unbiased for any distribution. Hmmm.....seems worth
thinking about some more.

Since sample mean is a sufficient statistic, it is the minimal variance
unbiased estimator for the parameter lambda.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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