Re: Curve fitting for a probability density function

bamakhr...@xxxxxxxxx wrote:
> 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.

By fitting a density using "least squares" I assume you mean minimizing
the squared deviations of the empirical and theoretical frequencies in
bins that you have defined. The generally preferred approach to density
estimation is to use "maximum likelihod estimation". The MLE estimates
for some densities have simple analytical forms and are described in
books such as "Statistical Distributions" by Evans, Hastings, and
Pea***.

.

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