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Function for converting Densities to Quantile Functions
dens2quantile( dens, dSup = seq(0, 1, length.out = length(dens)), qSup = seq(0, 1, length.out = length(dens)), useSplines = TRUE )
Q quantile function on qSup
density on dSup
support for Density domain - max and min values mark the boundary of the support.
support for quantile domain - must begin at 0 and end at 1
fit spline to the qd when doing the numerical integration (default: TRUE)
Functional Data Analysis for Density Functions by Transformation to a Hilbert space, Alexander Petersen and Hans-Georg Mueller, 2016
normaliseDensities
x <- seq(0,2,length.out =512) y <- rep(0.5,length.out =512) y.quantile <- dens2quantile(dens=y, dSup = x) # should equate # 2*seq(0, 1, length.out = 512)
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