moment (mathematics)

The moments of a function are certain quantitative measures related to the shape of the function’s graph.

The $k^{\text{th}}$ moment of a random variable $X$ is the expected value of the $k^{\text{th}}$ power of $X$:

$$m_k:=\mathbb{E}(X^k)$$

It’s like the taylor series in a way. Under certain conditions, the moments uniquely identify a probability distribution (the “moment problem”). More complex distributions may require more moments to fully describe them.

For a normal distribution, just two parameters fully specify it uniquely: the first moment (mean) and the variance (second central moment). Higher moments exist but are determined by these two.

https://de.wikipedia.org/wiki/Moment_(Stochastik)