Standard Score

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

$$Z = \frac{X - \mu}{\sigma}$$ (2.22)

, with $\mu$ as the mean and $\sigma$ as the standard deviation of $X$. The new random variable $Z$ has, by definition, a mean of zero and a unit variance.

It is possible to use this Z-score to filter potential outliers from the distribution.