Menu
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.
717
The normal distribution has excess kurtosis of zero. Any distribution that is peaked the same way as the normal distribution is sometimes called a mesokurtic distribution. An example of a mesokurtic distribution is the binomial distribution with the value of p close to 0.5.
Positive excess values of kurtosis (>3) indicate that a distribution is peaked and possess thick tails. Leptokurtic distributions have positive kurtosis values. A leptokurtic distribution has a higher peak (thin bell) and taller (i.e. fatter and heavy) tails than a normal distribution.
For kurtosis, the general guideline is that if the number is greater than +1, the distribution is too peaked. Likewise, a kurtosis of less than –1 indicates a distribution that is too flat. Distributions exhibiting skewness and/or kurtosis that exceed these guidelines are considered nonnormal." (Hair et al., 2017, p.
A normal distribution has skewness and excess kurtosis of 0, so if your distribution is close to those values then it is probably close to normal.
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
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
