RegulariseByAlpha: Function to regularise densities to have (larger) minimum...

In functionaldata/tDENS: Functional Data Analysis for Density Functions by Transformation to a Hilbert Space

Function to regularise densities to have (larger) minimum value

Description

If possible, regularises the input density y to have minimum density value is alpha. See details.

Usage

RegulariseByAlpha(x, y, alpha = 0.01)

Arguments

x	support of the density
y	values of the density
alpha	scalar to regularise with (default = 0.01) - this will be the minimum value of the regularised density, unless min(y) > alpha, in which case no regularisation will be performed

Details

If min(y) >= alpha or y is the uniform distribution, no regularisation is performed and y is returned. If alpha*diff(range(x)) > 1, the regularisation is not possible and an error is thrown. Otherwise, the regularised density is computed by adding an appropriate constant gam y, followed by renormalisation to have integral 1.

Value

dens density values on x

See Also

DeregulariseByAlpha,normaliseDensities

Examples

 x = seq(0,1,length.out=122)
 y = seq(0,2,length.out=122)
 z = RegulariseByAlpha(x=x, y=y, alpha = 0.1)
 

functionaldata/tDENS documentation built on June 12, 2025, 4:21 p.m.