hellingerpar {dad} | R Documentation |
Hellinger distance between Gaussian densities given their parameters
Description
Hellinger distance between two multivariate (p > 1
) or univariate (p = 1
) Gaussian densities given their parameters (mean vectors and covariance matrices if the densities are multivariate, or means and variances if univariate) (see Details).
Usage
hellingerpar(mean1, var1, mean2, var2, check = FALSE)
Arguments
mean1 |
|
var1 |
|
mean2 |
|
var2 |
|
check |
logical. When |
Details
The mean vectors (m1
and m2
) and variance matrices (v1
and v2
) given as arguments (mean1
, mean2
, var1
and var2
) are used to compute the Hellinger distance between the two Gaussian densities, equal to:
( 2 (1 - 2^{p/2} det(v1 v2)^{1/4} det(v1 + v2)^{-1/2} exp((-1/4) t(m1-m2) (v1+v2)^{-1} (m1-m2)) ))^{1/2}
If p = 1
the means and variances are numbers, the formula is the same ignoring the following operators: t (transpose of a matrix or vector) and det (determinant of a square matrix).
Value
The Hellinger distance between two Gaussian densities.
Be careful! If check = FALSE
and one covariance matrix is degenerated (multivariate case) or one variance is zero (univariate case), the result returned must not be considered.
Author(s)
Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Gilles Hunault, Sabine Demotes-Mainard
References
McLachlan, G.J. (1992). Discriminant analysis and statistical pattern recognition. John Wiley & Sons, New York .
See Also
hellinger: Hellinger distance between Gaussian densities estimated from samples.
Examples
m1 <- c(1,1)
v1 <- matrix(c(4,1,1,9),ncol = 2)
m2 <- c(0,1)
v2 <- matrix(c(1,0,0,1),ncol = 2)
hellingerpar(m1,v1,m2,v2)