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According to what I read from here, the kurtosis of a normal distribution should be around 3. However, when I use the kurtosis function provided by MATLAB, I could not verify it:

data1 = randn(1,20000);
v1 = kurtosis(data1)

It seems that the kurtosis of a normal distribution is around 0. I was wondering what's wrong with it. Thanks!

EDIT I am using MATLAB 2012b.

NPE
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feelfree
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    The odds are good that you have a kurtosis function somewhere on your path, that actually computes the excess kurtosis, so subtracting 3. This may be something you wrote long ago and forgot it, or that you downloaded, etc. –  Mar 07 '13 at 18:11
  • @woodchips You are right, and kurtosis function is not furnished with MATLAB if you do not have the statistics toolbox. – feelfree Mar 08 '13 at 14:54
  • The Normal distribution has a kurtosis of 3 but an *excess kurtosis* of 0. See [this reference](https://en.wikipedia.org/wiki/Kurtosis#Excess_kurtosis). – SecretAgentMan Dec 09 '18 at 19:19

1 Answers1

10

If it did that, this would be a strong indication that it was computing excess kurtosis, which is defined to be kurtosis minus three.

However, my MATLAB doesn't actually do that:

MATLAB>> data1 = randn(1,20000);
MATLAB>> kurtosis(data1)

ans =

    2.9825
NPE
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  • -1: The [official documentation](http://www.mathworks.com/help/stats/kurtosis.html) states: `Some definitions of kurtosis subtract 3 from the computed value, so that the normal distribution has kurtosis of 0. The kurtosis function does not use this convention.`, so apparently this is not the case. What do you have to say about that? – Eitan T Mar 07 '13 at 14:18
  • @EitanT: That's a good point. I was looking at a different MATLAB help page (`stats::kurtosis`), which was specifically talking about excess kurtosis. Now that I've actually tried the code, I can't reproduce OP's results. – NPE Mar 07 '13 at 14:23
  • I see. I've removed the downvote as the answer now is not incorrect, even though it does not resolve the question. _EDIT: apparently it did_ :) – Eitan T Mar 07 '13 at 14:27
  • The Normal distribution has a kurtosis of 3 but an *excess kurtosis* of 0. See [this reference](https://en.wikipedia.org/wiki/Kurtosis#Excess_kurtosis). – SecretAgentMan Dec 09 '18 at 19:19