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- For a trivial example, suppose I measured
where x had
an exponential distribution.
- Then the best estimate of the mean of y is obviously
and not
- The problem of estimating
is hardest for distributions
that have long tails.
- Then with a small probability, we will
generate events from the tail, but these will be way off the means,
and if included in calculation of mean, will distort
results in a finite sample.
Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu