View source: R/distl2dnormpar.R

distl2dnormpar | R Documentation |

`L^2`

distance between `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 `L^2`

-norm.

```
distl2dnormpar(mean1, var1, mean2, var2, check = FALSE)
```

`mean1, mean2` |
means of the probability densities. |

`var1, var2` |
variances ( |

`check` |
logical. When If the variables are univariate, it checks if the variances are not zero. |

Given densities `f_1`

and `f_2`

, the function `distl2dnormpar`

computes the distance between the `L^2`

-normed densities `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 `(4\pi)^{-p/4} det(var)^{-1/4}`

.

The `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)
```

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

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