Moments

Both mean and variance belong to a class of measures, called Moments

Raw Moments:

$${\mu }^{(j)}=E(X^j)={\int }_{-\infty }^{\infty }{x}^{j}f(x)dx$$

Central Moments:

$${\sigma }^{(j)}=E(X-\mu {)}^j={\int }_{-\infty }^{\infty }(x-\mu {)}^{j}f(x)dx$$

The Mean is also called the first (raw) Moments, and the Variance is called the second (central) Moments.

The third moment is about Skewness and the fourth moment is about Kurtosis. In the course ECON3002 Econometrics, we use the first two more.

In Chinese, we usually called it as “x 阶矩”, like “二阶距”