L^2-normed probability densities
L^2 distance between two multivariate (
p > 1) or univariate (dimension:
p = 1)
L^2-normed probability densities, estimated from samples, where a
L^2-normed probability density is the original probability density function divided by its
distl2dnorm(x1, x2, method = "gaussiand", check = FALSE, varw1 = NULL, varw2 = NULL)
the samples from the probability densities (see
string. It can be:
Notice that if
the bandwidths when the densities are estimated by the kernel method (see
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
L^2 distance between the two
Be careful! If
check = FALSE and one smoothing bandwidth matrix is degenerate, the result returned can not be considered.
Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Gilles Hunault, Sabine Demotes-Mainard
distl2d for the distance between two probability densities.
matdistl2dnorm in order to compute pairwise distances between several
require(MASS) m1 <- c(0,0) v1 <- matrix(c(1,0,0,1),ncol = 2) m2 <- c(0,1) v2 <- matrix(c(4,1,1,9),ncol = 2) x1 <- mvrnorm(n = 3,mu = m1,Sigma = v1) x2 <- mvrnorm(n = 5, mu = m2, Sigma = v2) distl2dnorm(x1, x2, method = "gaussiand") distl2dnorm(x1, x2, method = "kern") distl2dnorm(x1, x2, method = "kern", varw1 = v1, varw2 = v2)
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