hellinger function

Hellinger distance between Gaussian densities

Hellinger distance between two multivariate ($p > 1$) or univariate ($p = 1$) Gaussian densities (see Details).

hellinger(x1, x2, check = FALSE)

Arguments

• x1: a matrix or data frame of $n1$ rows (observations) and $p$ columns (variables) (can also be a tibble) or a vector of length $n1$.
• x2: matrix or data frame (or tibble) of $n2$ rows and $p$ columns or vector of length $n2$.
• check: logical. When TRUE (the default is FALSE) the function checks if the covariance matrices are not degenerate (multivariate case) or if the variances are not zero (univariate case).

Details

The Hellinger distance between the two Gaussian densities is computed by using the hellingerpar function and the density parameters estimated from samples.

Returns

Returns the $Hellinger$ distance between the two probability densities.

Be careful! If check = FALSE and one smoothing bandwidth matrix is degenerate, the result returned can not be considered.

References

McLachlan, G.J. (1992). Discriminant analysis and statistical pattern recognition. John Wiley & Sons, New York .

Author(s)

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

See Also

hellingerpar : Hellinger distance between Gaussian densities, given their parameters.

Examples

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)
hellinger(x1, x2)