# Kurtosis excessively high

1. May 25, 2012

### Zacku

Hello everyone,

I explain my problem: I have a set of histograms that do not appear normal (in the sense of the normal distribution). I need to convince a referee that it is in fact not normal. I have checked the skewness and the kurtosis and the former is at -2 and the latter is 60 !!!

I know these values seem non usual but I really double checked and I didn't make any mistake in the calculation of the third and fourth moments.

I would like to know if such a high value for the kurtosis is possible if the histogram is obviously non gaussian.

Just to give you an idea, I join a typical histogram that returns me these crazy values.

Thanks for any comment you would have.

Zacku

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2. May 25, 2012

### viraltux

Well, graphically you could plot on the top of the histogram the normal distribution so that the referee can see how different they are.

Checking the 3rd and 4th moments directly is not the way to go when testing for normality in a distribution. There are many different tests of normality like, for instance, the Jarque–Bera test which takes into account the the skewness and kurtosis matching a normal distribution. Just use one of the many you can find in the literature.

3. May 25, 2012

### SW VandeCarr

This is just a random sample I presume Single samples will rarely take the form of an ideal normal distribution unless the sample size is fairly large.. Moreover, there's a difference between normality and the Standard Normal distribution where the variance has a fixed relationship to the shape of the curve. Here, the variance is small which supports your estimate of the mean. The normality assumption would probably hold here, but as viralux says, there are specific tests for normality.

4. May 26, 2012

### Zacku

I will try other tests then. But just to specify that the histogram I showed is indeed a one sample histogram bu that contains 50000 points in it.

5. May 26, 2012

### SW VandeCarr

In that case, you might have more than one distribution. That is, two (or more) variables showing up as a joint distribution. You have an obvious major peak and some kind of additional activity to the right. Also, this might be some kind of decay pattern which would be skewed. What exactly is this?

Last edited: May 26, 2012