MakeLQDsample {fdadensity}

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
)

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)

Value

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

References

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

See Also

RegulariseByAlpha,dens2lqd

Examples

 

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')