# st: RE: Jarque - Bera

 From "Nick Cox" To Subject st: RE: Jarque - Bera Date Tue, 1 Jul 2008 17:49:53 +0100

```What econometricians or applied economists, it seems, know as a Jarque-Bera test -- puzzlingly, as the idea is much older than their publication -- is based on scaling sample skewness and kurtosis by their asymptotic standard errors as a test for normality [meaning, Gaussianity]. As even if the parent distribution really is Gaussian the sampling distributions approach asymptotic distributions very very slowly this has long struck me as dubious.

Nevertheless a -search- for Jarque-Bera shows that such tests are available after
-vecnorm- or -varnorm-, which may be what you want.

In general I assert that the best way to examine distributions for normality or its lack is to use probability plots as through -qnorm-.

Those who want a formal test regardless will find -swilk- to offer one. For various reasons I prefer, as a formal test, the Doornik-Hansen test available in -omninorm- from SSC.

It is instructive to fire up the auto dataset and then look at some results.

. omninorm price-foreign , marginals allobs

------------------------------------------------------------------------------
variable |         n        D-H    P-value       asy.    P-value
-----------------------+------------------------------------------------------
Price |        74    91.7602     0.0000    43.9215     0.0000
Mileage (mpg) |        74    12.3662     0.0021    14.0319     0.0009
Repair Record 1978 |        69     0.0491     0.9757     0.3353     0.8456
Headroom (in.) |        74     2.3717     0.3055     2.1766     0.3368
Trunk space (cu. ft.) |        74     1.9143     0.3840     2.0233     0.3636
Weight (lbs.) |        74     3.3193     0.1902     2.6670     0.2636
Length (in.) |        74     3.4545     0.1778     2.8531     0.2401
Turn Circle (ft.)  |        74     2.0574     0.3575     2.0198     0.3643
Displacement (cu. in.) |        74    13.1208     0.0014     5.5196     0.0633
Gear Ratio |        74     4.4838     0.1063     3.0799     0.2144
Car type |        74   234.1428     0.0000    14.2417     0.0008
------------------------------------------------------------------------------

On this test the -rep78- variable qualifies as most nearly normal and the -foreign- variable as most clearly non-normal!

Nick
n.j.cox@durham.ac.uk

matteorolla84@libero.it

in Stata can I use Jarque - Bera statistic? Are there other tests to prove
the normality of a distribution?

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```

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