Curve fitting for a probability density function

Hi,
I am working on a project and part of that project is building the
probability density function (pdf) for the distribution of the objects
sizes transmitted over HTTP protocol. The PDF which we are going to
generate should be fitted or estimated to a well known distribution
(i.e. exponential, pareto, log-normal, etc...). To do that, we are
computing the least squares for each distribution and choose the one
with minimum error. The result of the fit (or estimate) are the
parameters of the distribution. The problem which we are facing is that
the mean, variance, etc... for our data are different from the mean,
and variance calculated using the estimate. My question is: Since we
are doing the curve fitting for a PDF, should we consider the mean,
variance, skew, etc... in calculating the estimate or it is ok to have
an estimate which gives a mean and variance different from the actual
data. Another question is: In calculating the least squares, do we need
to set the weights to 1 or to the PDF itself since we are estimating a
PDF?

Regards,

--
Mohamed Bamakhrama
mohameda@xxxxxxxx

.

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