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

Title

robjb -- Brys, Hubert, and Struyf (2008) robust Jarque-Bera normality test

Syntax

robjb varname [if] [in] [, level(#) {skewness|kurtosis} right]

Description

robjb tests the normality of a given variable using a modified
Jarque-Bera (1980) statistic. Like the standard Jarque-Bera test, the
test is based on the variable's asymmetry (skewness) and tail
heaviness (kurtosis). However, rather than relying on classical
estimators for skewness and kurtosis, the robust Jarque-Bera statistic
relies on robust estimates of asymmetry and tail heaviness using
medcouple.

robjb, without options, relies both on asymmetry and on tail
heaviness to perform the test of normality. Using the option
skewness, the test is based exclusively on asymmetry; using
kurtosis, it is based on the heaviness of both tails; and using
right, the test is based only on the heaviness of the right tail.

When testing for normality, please see jb6 for the equivalent
classical estimators.

Options

level(#) specifies the confidence level for inference. The
default is level(0.95).

skewness specifies that a test exclusively based on skewness be run.

kurtosis specifies that a test exclusively based on the
heaviness of the tails be run.

right specifies that a test exclusively based on the heaviness
of the right tail be run.

Examples

Setup

. webuse auto

Testing for normality

. robjb price

Testing for normality exclusively relying on skewness

. robjb price, skewness

Testing for normality exclusively relying on the heaviness of the tails

. robjb price, kurtosis

Stored results

robjb stores the following in r():

Scalars

r(T) test statistic T

r(Chi2) critical value

r(dof) degrees of freedom

r(p) p-value

References

Brys, G., M. Hubert, and A. Struyf. 2008. Goodness-of-fit tests based on
a robust measure of skewness. Computational Statistics 23:
429-442.

Jarque, C. M., and A. K. Bera. 1980. Efficient tests for normality,
homoscedasticity and serial independence of regression residuals.
Economics Letters 6: 255-259.

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] swilk

Help: jb6 (if installed)