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RE: st: Computing medcouple


From   "Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Computing medcouple
Date   Thu, 13 Aug 2009 08:15:38 -0700

A few years ago I tried to develop a measure of skewness based on
percentiles:
"Skewness" = [(P75-P50)-(P50-P25)]/[P75-p25] 
And also similar ones based on P90 and P10.  I did fairly extensive
simulations and found that the P90, P10 based ones did a bit better in
expressing skewness.  In addition, the distribution of this was not
nicely behaved, but by log-transforming you would get a statistic that
looked very nicely normal.

In doing this I learned of the l-moments articles and was delighted that
Nick had already written a routine for this.

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
Sent: Wednesday, August 12, 2009 12:34 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Computing medcouple

This sounds a little similar in spirit to using L-moments to calculate a
skewness measure. The latter approach arguably has two features: it is
systematic and it is already implemented in Stata through -lmoments-
from SSC. 

As far as medcouple is concerned, you could compute it exactly or by
sampling. I've no code to offer. 

My prejudice here is that for most problems you would be better off
either transforming the data or using a graph form that discarded less
of the information than a box plot does. Otherwise put, if the data are
very skew you usually need to see more detail about the tails than a
boxplot provides. 

Nick 
n.j.cox@durham.ac.uk 


Ronnie Babigumira <rb.glists@gmail.com>

Vandervieren and Hubert (2004) present what they call a robust measure
of skewness using the medcouple

Given a distribution F, medcouple (MC(F)) is defined as

MC(F) = med h(xi,xj) given xi<med<xj

where

- h = 	(xj-m_F)-(m_F-xi)
	-----------------
		xj-xi

- m_F is the median of F

I would like to compute MC but dont know how to even start. Any pointers
will be much appreciated.

Ronnie

Reference

Vanderviere, E. & Huber, M. (2004). An adjusted boxplot for skewed
distributions. In J. Antoch 
(Ed.), COMPSTAT2004 Symposium: proceedings in computational statistics
(pp. 1933-1940). Heidelberg, 
Germany: Physica-Verlag.

The paper can be downloaded here
http://wis.kuleuven.be/stat/robust/Papers/boxplotCOMPSTAT04.pdf

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