# Re: st: Computing medcouple

 From Ronnie Babigumira To statalist@hsphsun2.harvard.edu Subject Re: st: Computing medcouple Date Fri, 14 Aug 2009 06:57:27 +0700

```Thanks for pointing me towards -lmoments-. Will take a look at it

Ronnie

Nick Cox wrote:
```
```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.
```
http://wis.kuleuven.be/stat/robust/Papers/boxplotCOMPSTAT04.pdf

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```
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