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FindDistributionParameters (and EstimatedDistribution) can use "MethodOfMoments" as its ParameterEstimator, but as far as I can tell it still requires you to give it the full observed data as its first argument. If I have the moments, but not the full data, is there any way to just pass the observed moments directly to FindDistributionParameters? Or do I have to write down the system of equations for the moments myself and then use FindRoot?

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    $\begingroup$ You will have to do this yourself but depending on the distribution it shouldn't be difficult. If you need help with a particular example you can always add it to your question. $\endgroup$
    – Andy Ross
    Commented Dec 5, 2014 at 5:24
  • $\begingroup$ Or -- a somewhat roundabout approach -- you could generate lots of data using the parameters you have and then use FindDistributedParameters on the data you have generated. $\endgroup$
    – bill s
    Commented Dec 5, 2014 at 15:23
  • $\begingroup$ @bills however if the moments they have are the parameters they wouldn't need to estimate. I think they have a situation where the parameters of interest are some function of the moments $\endgroup$
    – Andy Ross
    Commented Dec 5, 2014 at 18:49
  • $\begingroup$ @AndyRoss That's correct in my case -- if I knew how to generate the data I'd be done! It was just a bit annoying to write it myself, because writing the moments in terms of the parameters involved special functions, and I had to play with the form a bit to avoid over/underflows. I guess that means that I probably wouldn't have been able to use the default ParameterEstimator in any case though. $\endgroup$ Commented Dec 5, 2014 at 19:25

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There is an add-on for Mathematica, called MathStatica, which does exactly what you want, if I understood you right.

Find an example on www.mathstatica.com/examples and click on the left side on the item "Person Fitting." Ths is an excellent add-on which fits seamless into mma and extends its statistical capabilities.

Best regards Volker

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  • $\begingroup$ I was looking for something that would try to fit an arbitrary parametric form with an arbitrary number of free parameters (matching the number of moments). $\endgroup$ Commented Dec 10, 2014 at 17:44

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