Excess Kurtosis

Topics: Measure of Shape - Statistics

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(definition)

Given $X$ a variable and $k(X)$ its kurtosis, its excess kurtosis (also known as Fisher’s coefficient) is defined as:

$$k_3(X)=k(X)-3$$

Meaning §

Etymology

Mesokurtic comes from Ancient Greek μέσος (mésos, “middle”).

Leptokurtic comes from Ancient Greek λεπτός (leptós, “thin”).

Platykurtic comes from Ancient Greek πλατύς (platús, “flat”).

Excess kurtosis describes how arched the variable’s mass is. When $k_3(X)=0$, we say that $X$ is mesokurtic; a normal distribution is mesokurtic.

When $k_3(X)>0$, we say that $X$ is leptokurtic (in red):

(courtesy of Wikimedia Commons)

When $k_3(X)<0$, we say that $X$ is platykurtic (in red):

(courtesy of Wikimedia Commons)