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Choosing a Distribution from Skewness and Kurtosis

Article Quant Q&A · Author: Add
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Summary

The discussion asks how to model data with positive skewness and very high kurtosis, and how to calculate a time-specific distribution measure analogous to a normal z-score. It does not identify a particular distribution from those two statistics alone. Instead, the replies recommend fitting candidate distributions to the actual dataset and comparing their goodness of fit, for example with a tool that fits and ranks multiple parametric distributions.

The main caveat is that skewness and kurtosis describe only limited features of a sample; they do not reveal enough about its full shape to select a reliable model. The exchange gives no data, fitted parameters, comparison results, or procedure for computing the requested time-varying score after a distribution is selected. A trader or researcher would need to validate the fit on relevant data and define an appropriate standardized measure for the chosen distribution rather than assume the normal z-score carries over unchanged.

Key ideas

  • Skewness and kurtosis alone do not determine which probability distribution fits a dataset.
  • Fit plausible candidate distributions to the observed data and compare their goodness of fit.
  • Distribution choice depends on the data and the modeling context.
  • The discussion does not provide a fitted distribution or a method for calculating the requested time-specific score.

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# Distribution for High Kurtosis


# Distribution for High Kurtosis












Can you please advise which distribution to follow when your skewness is 0.28 and Kurtosis value is 51. Since it's leptokurtic and positively skewed I would like to fit distribution and also wanted to calculate distribution value at each time "t" just like we calculate Z score for Normal Distribution.

## Answer by JohnAndrews (score 4)

https://quant.stackexchange.com/a/3258

That can be a somewhat difficult question to answer, given that the context may yield different distributions. Nevertheless, I think that you could try to fit the best distribution algorithmically. For instance, lately I found this package at Matlab file exchange:

Finding the best distribution that fits the data Link

> (...) This is where Mike's allfitdist comes into play. Statistics Toolbox supports a long list of distributions, including parametric and nonparametric distributions. allfitdist fits all valid parametric distributions to the data and sorts them using a metric you can use to compare the goodness of the fit. (...)

Hope that this helps. Let me know whether it worked for you!

## Answer by pyCthon (score 1)

https://quant.stackexchange.com/a/3262

I think the best answer is to test different distributions with your specific data set and see which fits the data the best... skewness and kurtosis are just a small piece of information , there is still a good deal of information we don't know and won't have with out having the data set in front of us

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.