The \(n\)th moment of variable \(X\) is defined as:
\(E[X^n]=\sum_i x_i^n P(x_i)\)
The mean is the first moment.
The \(n\)th central moment of variable \(X\) is defined as:
\(\mu_n=E[(X-E[X])^n]=\sum_i (x_i-E[X])^n P(x_i)\)
The variance is the second central moment.
The \(n\)th standardised moment of variable \(X\) is defined as:
\(\dfrac{E[(X-E[X])^n]}{(E[(X-E[X])^2]^\frac{n}{2}}=\dfrac{\mu_n}{\sigma^n}\)
Kertosis is the third standardised moment.
Skew is the fourth standardised moment.