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