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RE: Adding multi-D skewness, kurtosis, and Jarque Bera test

From: Pebay, Philippe P
Subject: RE: Adding multi-D skewness, kurtosis, and Jarque Bera test
Date: Tue, 30 Nov 2010 16:16:47 -0700


Thank you for the prompt response and the interest for the statistics functions 
I mentioned earlier.

Yes, I see then that it probably makes more sense to contribute these functions 
to Octave-Forge. For instance, I have made the signature of the statistical 
test match that of the other statistical tests currently available in Octave, 
and not in Matlab.
For instance, the multi-dimensional Jarque-Bera-Srivastave test signature is:

function [PVAL, JBS, DF] = multi_jbtest( M )

  % M is a matrix of input data: observations per row, variables per column
  % PVAL is the Jarque-Bera-Srivastava normality test p-value
  % JBS  is the corresponding Jarque-Bera-Srivastava statistic
  % DF   is the corresponding number of degrees of freedom

For the multi-skewness and multi-kurtosis it simply is:

function [BS1, BS2] = multi_skew_kurt( M )

  % M is a matrix of input data: observations per row, variables per column
  % BS1 is the multi-dimensional skewness in the Srivastava sense
  % BS2 is the multi-dimensional kurtosis in the Srivastava sense

I cannot unfortunately send you the code right now, because at Sandia we must 
submit to an internal review process before we can release any open-source 
code. However, as we now know that there might be some interest for 
Octave-Forge, I will initiate this review process so I can show you the code, 
which is short anyway: 26 lines for multi_jbtest.m and 31 for 
multi_skew_kurt.m, as they both leverage existing Octave capabilities (SVD in 

I will send the code as soon as it is approved for public release.

Thanks again for your interest.

Philippe Pébay
Sandia National Laboratories

From: Søren Hauberg address@hidden
Sent: Tuesday, November 30, 2010 11:04 AM
To: Pebay, Philippe P
Cc: address@hidden
Subject: Re: Adding multi-D skewness, kurtosis, and Jarque Bera test


tir, 30 11 2010 kl. 10:40 -0800, skrev Philippe Pébay:
> We have written the following Octave functions providing the following 
> capabilities:
> 1. A function calculating the multi-dimensional skewness and kurtosis of an 
> input data
> set, based on M.S. Srivastava, "A Measure of Skewness and Kurtosis and a 
> Graphical Method
> for Assessing Multivariate Normality", Stat. & Prob. Letters, 2 (1984)
> 2. A function providing the multi-dimensional extension of the Jarque-Bera 
> test for
> normality of observations, based on K. Koizumi et al, "On Jarque-Bera Tests 
> for Assessing
> Multivariate Normality", J. Statistics: Advances in Theory and Application, 1 
> (2009)
> We would like to contribute these functions to either Octave or Octave-Forge 
> and would
> appreciate feedback as to which of the two is the most appropriate for these 
> functions.

These sounds like good contributions to me. A couple of comments:

      * It's easier for us to give comments if you send the code :-)
      * In general, there is a trend towards moving functions from
        Octave to Octave-Forge if these are not in core Matlab. I think
        it was previously discussed if we should move functions like
        'kurtosis' to Octave-Forge. So, it could be that your
        contributions are best suited for Octave-Forge.


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