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This question was inspired by a comment made by @whuber in response to this question regarding the use of distributional tests.

The comment stated there is never any reason to use [the Jarque-Bera test]. I'm looking for a comprehensive exploration of this, which I assume will related to other distributional tests.

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    $\begingroup$ I was exaggerating a bit to make a point: the JB test is simple to implement and therefore might be preferred for very quick and dirty work by those who only have a calculator without any plotting capabilities. $\endgroup$ – whuber Jan 24 '19 at 13:19
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I'm no expert on this subject, but there seems to be quite some blog posts and even publications on this subject.

I would suggest reading those, but in general it seems that the test might be biased and have low power when using small samples, and when the original distribution is short-tailed.

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I would argue the opposite... and that as far as tests for Normal distributions are concerned, Jarque-Bera is the most transparent and explicit since it captures a combination of Skewness and Kurtosis which are the two dimensions that capture divergence from a Normal distribution. And, to my knowledge it does that better than any other tests for Normal distribution.

One may argue that Jarque-Bera is too sensitive to sample size. The larger the sample the more a trivial divergence from the Normal Distribution will become statistically significant. However, this is true of all such Normal Distribution tests. Actually, this is true of the entire body of hypothesis testing that relies on p-value instead of Effect Size.

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    $\begingroup$ Isn't it also true that the asymptotic distribution of the Jarque-Bera doesn't become reliable until sample sizes ~300? - as stated by @Glen_b in a comment here $\endgroup$ – Ed P Jan 31 '19 at 22:41
  • $\begingroup$ I can't comment on that. However, before pronouncing the JB test dead, it should be benchmarked against its competitors. In isolation, stating a test is good or bad is not informative until you can actually rank that test against its alternatives. And, I would venture that the JB test on a relative basis holds up just fine. In the end, all tests have their flaws, but many are still pretty informative. I would think the JB one falls into that category. $\endgroup$ – Sympa Feb 1 '19 at 4:58

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