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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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st: Computing medcouple***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**References**:**Re: st: Computing medcouple***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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