D2.dist: Pairwise Squared Generalized Mahalanobis Distances
In biotools: Tools for Biometry and Applied Statistics in Agricultural Science

Description Usage Arguments Value Author(s) References See Also Examples

Function to calculate the squared generalized Mahalanobis distance between all pairs of rows in a data frame with respect to a covariance matrix. The element of the i-th row and j-th column of the distance matrix is defined as

D_{ij}^2 = (\bold{x}_i - \bold{x}_j)' \bold{Σ}^{-1} (\bold{x}_i - \bold{x}_j)

1	D2.dist(data, cov, inverted = FALSE)

`data`	a data frame or matrix of data (n x p).
`cov`	a variance-covariance matrix (p x p).
`inverted`	logical. If `FALSE` (default), `cov` is supposed to be a variance-covariance matrix.

An object of class "dist".

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

Mahalanobis, P. C. (1936) On the generalized distance in statistics. Proceedings of The National Institute of Sciences of India, 12:49-55.

dist, singh

# Manly (2004, p.65-66)
x1 <- c(131.37, 132.37, 134.47, 135.50, 136.17)
x2 <- c(133.60, 132.70, 133.80, 132.30, 130.33)
x3 <- c(99.17, 99.07, 96.03, 94.53, 93.50)
x4 <- c(50.53, 50.23, 50.57, 51.97, 51.37)
x <- cbind(x1, x2, x3, x4)
Cov <- matrix(c(21.112,0.038,0.078,2.01, 0.038,23.486,5.2,2.844,
	0.078,5.2,24.18,1.134, 2.01,2.844,1.134,10.154), 4, 4)
D2.dist(x, Cov)

# End (not run)