matdistl2dnormpar function

Matrix of $L^2$ distances between $L^2$-normed Gaussian densities given their parameters

Computes the matrix of the $L^2$ distances between several multivariate ($p > 1$) or univariate ($p = 1$) $L^2$-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 Gaussian density is the original probability density function divided by its $L^2$-norm.

matdistl2dnormpar(meanL, varL)

Arguments

• meanL: list of the means ($p = 1$) or vector means ($p > 1$) of the Gaussian densities.
• varL: list of the variances ($p = 1$) or covariance matrices ($p > 1$) of the Gaussian densities.

Returns

Positive symmetric matrix whose order is equal to the number of densities, consisting of the pairwise distances between the $L^2$-normed probability densities.

Author(s)

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

See Also

distl2dnormpar.

matdistl2dpar for the distance matrix between Gaussian densities, given their parameters.

matdistl2dnorm for the distance matrix between normed probability densities which are estimated from the data.

Examples

data(roses)
    
    # Multivariate:
    X <- roses[,c("Sha","Den","Sym","rose")]
    summary(X)
    mean.X <- as.list(by(X[, 1:3], X$rose, colMeans))
    var.X <- as.list(by(X[, 1:3], X$rose, var))
    
    # Gaussian densities, given parameters
    matdistl2dnormpar(mean.X, var.X)

    # Univariate :
    X1 <- roses[,c("Sha","rose")]
    summary(X1)
    mean.X1 <- by(X1$Sha, X1$rose, mean)
    var.X1 <- by(X1$Sha, X1$rose, var)
    
    # Gaussian densities, given parameters
    matdistl2dnormpar(mean.X1, var.X1)