*! version 1.1.0 7Mars2013
help medcouple (SJ15-1: st0001)

Title

medcouple -- Medcouple measure of asymmetry and tail heaviness

Syntax

medcouple varname [if] [in] [, lmc rmc nomc]

Description

medcouple estimates medcouple, a robust measure of asymmetry and tail
heaviness.

medcouple, without options, estimates the standard medcouple, which is a
robust measure of asymmetry. Its value is always between -1 and 1. The
medcouple is zero for symmetric distributions, while it is positive and
negative for, respectively, right- and left-tailed distributions.

The options lmc and rmc can be used to calculate the left and
right medcouple, respectively. The left medcouple is a robust measure for the
heaviness of the left tail. It estimates the medcouple for all observations
smaller than the median. It thus measures the asymmetry of the lower half of
the distribution, which is a measure of the heaviness of the left tail. The
right medcouple does exactly the same for all values above the median and is
thus a measure of the heaviness of the right tail.

To interpret the left and right medcouple, one should note that both sides of
the distribution are typically skewed, leading to values different from zero.
For both the left and right medcouple, higher values indicate heavier tails.
For comparison, the right medcouple of the standard normal is 0.2. Values
above 0.2 thus indicate a right tail that is heavier than that of the normal.

When estimating asymmetry and heaviness of the tails, please see
[R] summarize for classical estimators.

Options

lmc specifies calculating the medcouple only for observations smaller
than the median. This is an indicator of the heaviness of the left tail.

rmc specifies calculating the medcouple only for observations larger
than the median. This is an indicator of the heaviness of the right tail.

nomc specifies not to calculate the global medcouple. This is useful
when one is interested in only the tail heaviness.

Example

Setup

. webuse auto

Estimating the medcouple measure of asymmetry

. medcouple price, lmc rmc

Stored results

medcouple stores the following in e():

Scalars

e(mc) medcouple statistic

e(lmc) left medcouple (if called by the option)

e(rmc) right medcouple (if called by the option)

Functions

e(sample) marks estimation sample

Authors

Wouter Gelade

University of Namur

CRED

Namur, Belgium

wouter.gelade@unamur.be

Vincenzo Verardi

University of Namur

CRED

Namur, Belgium

and Université libre de Bruxelles

ECARES and iCite

Brussels, Belgium

vincenzo.verardi@unamur.be

Catherine Vermandele

Université libre de Bruxelles

LMTD

Brussels, Belgium

catherine.vermandele@ulb.ac.be

Also see

Article: Stata Journal, volume 15, number 1: st0001

Manual: [R] summarize