mahalanobis {stats} | R Documentation |

## Mahalanobis Distance

### Description

Returns the squared Mahalanobis distance of all rows in `x`

and the
vector `\mu`

= `center`

with respect to
`\Sigma`

= `cov`

.
This is (for vector `x`

) defined as

`D^2 = (x - \mu)' \Sigma^{-1} (x - \mu)`

### Usage

```
mahalanobis(x, center, cov, inverted = FALSE, ...)
```

### Arguments

`x` |
vector or matrix of data with, say, |

`center` |
mean vector of the distribution or second data vector of
length |

`cov` |
covariance matrix ( |

`inverted` |
logical. If |

`...` |
passed to |

### See Also

### Examples

```
require(graphics)
ma <- cbind(1:6, 1:3)
(S <- var(ma))
mahalanobis(c(0, 0), 1:2, S)
x <- matrix(rnorm(100*3), ncol = 3)
stopifnot(mahalanobis(x, 0, diag(ncol(x))) == rowSums(x*x))
##- Here, D^2 = usual squared Euclidean distances
Sx <- cov(x)
D2 <- mahalanobis(x, colMeans(x), Sx)
plot(density(D2, bw = 0.5),
main="Squared Mahalanobis distances, n=100, p=3") ; rug(D2)
qqplot(qchisq(ppoints(100), df = 3), D2,
main = expression("Q-Q plot of Mahalanobis" * ~D^2 *
" vs. quantiles of" * ~ chi[3]^2))
abline(0, 1, col = 'gray')
```

[Package

*stats*version 4.4.1 Index]