I have seen several models for estimating the expected value and variance of a distribution. I am curious, to learn if anyone has looked at models that extend beyond these first two moments especially skew & kurtosis. I will be grateful if you could share your thoughts.

  • 1
    $\begingroup$ Do you mean forecasting in the time series sense? Are you looking to build models for time varying skewness and kurtosis? $\endgroup$ Jan 29 '15 at 5:22
  • $\begingroup$ It is unclear what you are asking. $\endgroup$
    – Tim
    Jan 29 '15 at 8:01

The Pearson family and Johnson family are both based on the first 4 moments ... and, in particular, expressed in terms of skewness and kurtosis. Both approaches generally work very well provided skewness and kurtosis are not too large and your model is unimodal.

For application and much more detail, see, for instance:

  • Chapter 5 of our book: Rose and Smith, Mathematical Statistics with Mathematica $\rightarrow$ a free download is available at: http://www.mathstatica.com/book/bookcontents.html , or

  • Stuart and Ord (1994), Kendall's Advanced Theory of Statistics (6th edition) - Chapter 6.

For an example of Johnson fitting on stackexchange, see this question: Robust distribution fitting?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.