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.