L^2-normed Gaussian densities given their parameters
L^2 distance between two multivariate (
p > 1) or univariate (dimension:
p = 1)
L^2-normed Gaussian densities, given their parameters (mean vectors and covariance matrices if the densities are multivariate, or means and variances if univariate) where a
L^2-normed probability density is the original probability density function divided by its
distl2dnormpar(mean1, var1, mean2, var2, check = FALSE)
means of the probability densities.
If the variables are univariate, it checks if the variances are not zero.
f_2, the function
distl2dnormpar computes the distance between the
f_1 / ||f_1|| and
f_2 / ||f_2||:
2 - 2 <f_1, f_2> / (||f_1|| ||f_2||)
For some information about the method used to compute the
L^2 inner product or about the arguments, see
l2dpar; the norm
||f|| of the multivariate Gaussian density
f is equal to
L^2 distance between the two
L^2-normed Gaussian densities.
Be careful! If
check = FALSE and one variance matrix is degenerated (or one variance is zero if the densities are univariate), the result returned must not be considered.
Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Gilles Hunault, Sabine Demotes-Mainard
distl2dpar for the distance between two probability densities.
matdistl2d in order to compute pairwise distances between several densities.
u1 <- c(1,1,1); v1 <- matrix(c(4,0,0,0,16,0,0,0,25),ncol = 3); u2 <- c(0,1,0); v2 <- matrix(c(1,0,0,0,1,0,0,0,1),ncol = 3); distl2dnormpar(u1,v1,u2,v2)
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