Kurtosis
Kurtosis (the term first used by Pearson, 1905) measures
the "peakedness" of a distribution. If the kurtosis
is clearly different than 0, then the distribution is either flatter or
more peaked than normal; the kurtosis
of the normal distribution is
0.
A kurtosis greater
than 0 implies that the distribution has a sharper peak around the mean
with longer, fatter tails. This type of distribution is called leptokurtic.
A kurtosis less than 0 implies that the distribution has
a more rounded peak near the mean with shorter thinner tails. This type
of distribution is called platykurtic. A normal distribution is called
mesokurtic.
Kurtosis is computed as:
Kurtosis =
[n*(n+1)*M4
- 3*M2*M2*(n-1)] / [(n-1)*(n-2)*(n-3)*s4]
where:
Mj |
is equal to: S(xi-Meanx) j |
n |
is the valid number of cases |
s4 |
is the standard deviation (sigma) raised to the fourth power |
See also: Descriptive
Statistics Overview.