Standard Score

An alternative formulation of the Mahalanobis distance is the Standard Score. A random variable $X$ is standardized using its empirical statistics by applying the transformation

$$Z = \frac{X - \mu}{\sigma}$$ (2.24)

where $\mu$ is the mean and $\sigma$ is the standard deviation of $X$. By definition, the new random variable $Z$ has zero mean and unit variance.

This Z-score can be used to filter potential outliers from the distribution.