# Mahalanobis Distance

From Open Risk Manual

## Definition

The **Mahalanobis Distance** of an observation of random vector X that is sampled from a multivariate distribution is a measure of its "distance" from the mean of the distribution

## Formula

where

- X is a vector of observations
- is the covariance matrix
- is the mean vector

If the covariance matrix is the identity matrix, the Mahalanobis distance reduces to the Euclidean distance