l2dpar {dad} | R Documentation |
L^2
inner product of Gaussian densities given their parameters
Description
L^2
inner product of 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).
Usage
l2dpar(mean1, var1, mean2, var2, check = FALSE)
Arguments
mean1 |
|
var1 |
|
mean2 |
|
var2 |
|
check |
logical. When |
Details
Computes the inner product of two Gaussian densities, equal to:
(2\pi)^{-p/2} det(var1 + var2)^{-1/2} exp(-(1/2) t(mean1 - mean2) (var1 + var2)^{-1} (mean1 - mean2))
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 L^2
inner product 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
M. Wand and M. Jones (1995). Kernel Smoothing. Chapman and Hall, London.
See Also
l2d for parametrically estimated Gaussian densities or nonparametrically estimated densities, given 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)
l2dpar(m1,v1,m2,v2)