Re: 3-parameter Gamma and Weibull distribution

Maciej wrote:
Do exist m-files that I could use to fit 3-parameter distribution: Gamma and Weibull

Maciej, the most common way to fit univariate distributions is by maximum likelihood, but with a threshold parameter, like the 3-param Gamma and Weibull have, maximum likelihood often doesn't give plausible fits (Weibull), and sometimes never works at all (lognormal). In the case of the lognormal, the problem is that the ML estimate of the threshold is the smallest observation, and the estimated distribution is degenerate at that point. I think the Weibull has similar cases.

So people have come up with various ad-hoc methods to overcome this, the ones I've seen are mostly specific to one distribution. I know that for the Weibull, there have been a variety of methods proposed, not sure about the gamma. You may find something on MATLAB Central along those lines.

This demo

<http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/cdffitdemo.html>

illustrates a general method for estimating a threshold parameter. You may find it helpful. Just by coincidence, gamma and Weibull are two of the examples.

- Peter Perkins
The MathWorks, Inc.
.

Relevant Pages

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