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During the execution of a script I wrote, the answer is a stochastic variable with an unknown distribution.

While I do not know the distribution of the answer, I do have access to the following information:

  • Moments can be approximated pretty well with standard quadratures
  • Random values can be evaluated very fast
  • Most of the time I have a rough estimation of the support of the distribution

What would be the best approach (as in: best approximation given a fixed time bound) to finding an estimation for the probability distribution?

I could draw random values, and use the resulting histogram as an approximation, but this is slow converging. I have not yet tried entropy maximizing algorithms, but I suppose those could work as well.

Does anyone have a better suggestion?

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Consider kernel density estimation or orthogonal series density estimation (e.g., wavelet density estimation).

Do you know the support (non-zero domain) of the density?

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    Smoothing is not superfluous; it is done to avoid [overfitting](http://en.wikipedia.org/wiki/Overfitting).2011-11-19