# getWFmean: Wasserstein Frechet Mean Computation In fdadensity: Functional Data Analysis for Density Functions by Transformation to a Hilbert Space

## Description

Function for computing the Wasserstein Frechet mean through quantile density averaging

## Usage

 ```1 2 3 4 5 6 7 8``` ```getWFmean( dmatrix, dSup, N = length(dSup), qdSup = seq(0, 1, length.out = N), useAlpha = FALSE, alpha = 0.01 ) ```

## Arguments

 `dmatrix` matrix of density values on dSup - must be strictly positive and each row must integrate to 1 `dSup` support (grid) for Density domain `N` desired number of points on a [0,1] grid for quantile density functions; default length(dSup) `qdSup` support for LQ domain - must begin at 0 and end at 1; default [0,1] with N-equidistant support points `useAlpha` should regularisation be performed (default=FALSE) `alpha` Scalar to regularise the supports with (default=0.01)

## Value

wfmean the Wasserstein-Frechet mean density

## References

Functional Data Analysis for Density Functions by Transformation to a Hilbert space, Alexander Petersen and Hans-Georg Mueller, 2016

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```x <- seq(0,1,length.out = 101) # linear densities on (0, 1) y <- t(sapply(seq(0.5, 1.5, length.out = 10), function(b) b + 2*(1 - b)*x)) wfmean = getWFmean(y, x) # Plot WF mean with Euclidean Mean matplot(x, t(y), ylab = 'Density', type = 'l', lty = 1, col = 'black') lines(x, wfmean, lwd = 2, col = 'red') lines(x, colMeans(y), lwd = 2, col = 'blue') legend('topright', col = c('black', 'red', 'blue'), lwd = c(1, 2, 2), legend = c('Densities', 'WF Mean', 'Euclidean Mean')) ```

fdadensity documentation built on Dec. 5, 2019, 9:07 a.m.