[Octave-bug-tracker] [bug #36718] moment, skewness and kurtosis

[Alexander Barth]

URL:
  <http://savannah.gnu.org/bugs/?36718>

                 Summary: moment, skewness and kurtosis
                 Project: GNU Octave
            Submitted by: abarth
            Submitted on: Sun 24 Jun 2012 08:46:06 PM GMT
                Category: Interpreter
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Matlab Compatibility
                  Status: None
             Assigned to: None
         Originator Name: Alexander Barth
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.6.0
        Operating System: GNU/Linux

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Details:

In matlab (R2010a), I get: 

>> x = [1:5].^2;
>> moment(x,3)
ans =
  303.6000
>> skewness(x)
ans =
    0.4693

% this is (std(x,1)^(-3)) * mean ((x - mean(x)).^3)
>> kurtosis(x)
ans =
    1.8394

while in octave 3.6.0:

moment(x,3)  
ans =  4103

In matlab, moments are central while octave uses raw moment per default
(central moments can be activated with moment(x,3,'c'))

skewness(x)
ans =  0.33580

This is (std(x,0)^(-3)) * mean ((x - mean(x)).^3). The normalization of std is
thus different.

kurtosis(x)
ans = -1.8228

Again a different normalization of std, and a minus 3 in octave (excess
kurtosis).

Concerning the normalization of std (1/n versus 1/(n-1)), I have seen at least
a third definition on the web.
(http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm). What a
mess!

I would propose that we follow the matlab convention here.

Attached are some patches, with the necessary changes in the calculations to
the functions (but help text and test are not updated yet, ... bed time now).



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File Attachments:


-------------------------------------------------------
Date: Sun 24 Jun 2012 08:46:06 PM GMT  Name: kurtosis.m.patch  Size: 708B  
By: abarth

<http://savannah.gnu.org/bugs/download.php?file_id=26100>
-------------------------------------------------------
Date: Sun 24 Jun 2012 08:46:06 PM GMT  Name: skewness.m.patch  Size: 668B  
By: abarth

<http://savannah.gnu.org/bugs/download.php?file_id=26101>
-------------------------------------------------------
Date: Sun 24 Jun 2012 08:46:06 PM GMT  Name: moment.m.patch  Size: 751B   By:
abarth

<http://savannah.gnu.org/bugs/download.php?file_id=26102>

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