central moment

Central Moment

A central moment is a statistical measure that describes a distribution relative to its mean, by centering the data around zero first. For a random variable $X$:

$${\mu }_n=E[(X-\mu {)}^n]$$

where $n$ is the order of the moment and $\mu$ is the mean of $X$.

Common central moments:

• First (n=1): Always 0 (by definition)
• Second (n=2): Variance
• Third (n=3): Skewness (asymmetry)
• Fourth (n=4): Kurtosis (tailedness)