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Re: st: Computing medcouple


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Computing medcouple
Date   Wed, 12 Aug 2009 20:33:32 +0100

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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