MakeLQDsample: Convenience function for converting densities to log-quantile densities

Description

See 'dens2lqd' and 'RegulariseByAlpha' for more details. This function first (transforms the densities in 'dmatrix' to log quantile density functions, optionally followed by regularisation.

Usage

MakeLQDsample(
  dmatrix,
  dSup,
  lqdSup = seq(0, 1, length.out = length(dSup)),
  useAlpha = FALSE,
  alpha = 0.01
)

Value

list with 'LQD', a matrix of log quantile density functions, and 'lqdSup' that matches the input argument

Arguments

dmatrix: Matrix holding the density values on dSup - all rows must be strictly positive and integrate to 1
dSup: Support (grid) for Density domain
lqdSup: Support grid for lqd domain (default = seq(0, 1, length.out = length(dSup)))
useAlpha: should regularisation be performed (default=FALSE)
alpha: Scalar to regularise the supports with (default=0.01)

References

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

Examples

Run this code

 

x <- seq(0,1,length.out = 101)
# some log quantile densities on (0, 1)
y <- t(sapply(seq(0.5, 1.5, length.out = 10), function(b) -log(b^2 + 4*(1-b)*x)/2)) 

# Get densities

y.dens = MakeDENsample(qmatrix = y, lqdSup = x, dSup = x)$DEN
matplot(x, t(y.dens), ylab = 'Density', type = 'l', lty = 1, col = 'black')

# Get LQDs Back

y.lqd = MakeLQDsample(y.dens, lqdSup = x, dSup = x)
# These should match
matplot(y.lqd$lqdSup, t(y.lqd$LQD), ylab = 'LQD', type = 'l', lty = 1, col = 'blue')
matplot(x, t(y), ylab = 'LQD', type = 'l', lty = 1, col = 'red')