# distl2dpar: L^2 distance between Gaussian densities given their... In dad: Three-Way / Multigroup Data Analysis Through Densities

 distl2dpar R Documentation

## `L^2` distance between Gaussian densities given their parameters

### Description

`L^2` distance between two multivariate (`p > 1`) or univariate (dimension: `p = 1`) Gaussian densities, given their parameters (mean vectors and covariance matrices if the densities are multivariate, or means and variances if univariate).

### Usage

``````distl2dpar(mean1, var1, mean2, var2, check = FALSE)
``````

### Arguments

 `mean1, mean2` means of the probability densities. `var1, var2` variances (`p` = 1) or covariance matrices (`p` > 1) of the probability densities. `check` logical. When `TRUE` (the default is `FALSE`) the function checks if the covariance matrices are not degenerate, before computing the inner product. If the variables are univariate, it checks if the variances are not zero.

### Details

The function `distl2dpar` computes the distance between two densities, say `f_1` and `f_2`, from the formula:

`||f_1 - f_2||^2 = <f_1, f_1> + <f_2, f_2> - 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`.

### Value

The `L^2` distance between the two 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.

### Author(s)

Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Gilles Hunault, Sabine Demotes-Mainard

`matdistl2d` in order to compute pairwise distances between several densities.

### Examples

``````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);
distl2dpar(u1,v1,u2,v2)
``````

dad documentation built on Aug. 30, 2023, 5:06 p.m.