 Skewness

For a real random variable with finite third absolute moment and positive variance ${\sigma }^2$, its skewness is ${\gamma }_1=\mathbb{E}[(X-\mathbb{E}X{)}^3]/{\sigma }^3$. It is dimensionless and unchanged by positive rescaling or translation; a reflection reverses its sign. A symmetric distribution has zero skewness, but the converse fails: values $-2,1,3$ with probabilities $0.4,0.5,0.1$ have mean zero and third moment zero without symmetry. Constant variables have no defined standardized skewness because $\sigma =0$. The cosmological reduced skewness $S_3=⟨{\delta }^3⟩/{\sigma }^4$ uses a different normalization.

Skewness is a statistical measure that describes the asymmetry of a distribution. It indicates the direction and degree of distortion from the symmetrical bell curve of a normal distribution. In essence, skewness quantifies how much the distribution leans to one side compared to the other. There are three types of skewness: 1. **Positive Skewness (Right Skewness)**: In this case, the tail on the right side of the distribution is longer or fatter than the left side.