sphere.hdr {HDiR} | R Documentation |
Computation of HDRs for a spherical density and of general level sets for spherical real-valued functions
Description
This function computes HDRs of a spherical density and general level sets for real-valued functions defined on the unit sphere.
Usage
sphere.hdr(f,tau=NULL,level=NULL,nborder=1000,tol=0.1,
mesh=40,deg=6,plot.hdr=TRUE,col=NULL)
Arguments
f |
Object of class |
tau |
Numeric probability. According to Saavedra-Nieves and Crujeiras (2021), |
level |
Numeric threshold of the HDR or of the general level set provided by the user. If |
nborder |
Maximum number of HDRs boundary points to be represented. Default |
tol |
Tolerance parameter to determinate the boundary of HDRs. Default |
mesh |
A numeric value 10, 20 or 40 indicating the 3D cartesian mesh used for numerical integration on the unit shere. Default |
deg |
Integer string indicating the degree (from 0 to 6) of the quadrature rules for triangles on the sphere for numerical integration. Default |
plot.hdr |
Logical string. If |
col |
Color number for plotting the boundary of the HDR. Default |
Details
A detailed definition of directional HDRs for a density is given in Saavedra-Nieves and Crujeiras (2021). Note that numerical integration on the sphere is used to compute the threshold of HDR when tau
is provided.
Value
If tau
is provided, a list with the next components:
hdr |
A matrix of rows of points on the HDR boundary. |
prob.content |
Probability coverage |
level |
Threshold associated to the probability content |
If level
is provided, a list with the next components:
levelset |
A matrix of rows of points on the level set boundary. |
level |
Threshold of the level set. |
Author(s)
Paula Saavedra-Nieves, Rosa M. Crujeiras and Andrés Prieto.
References
Saavedra-Nieves, P. and Crujeiras, R. M. (2021). Nonparametric estimation of directional highest density regions. Advances in Data Analysis and Classification, 1-36.
Examples
#HDR of model 8 in library HDiR
f1<-function(x){return(dspheremix(x,model=8))}
sphere.hdr(f1,tau=0.5,mesh=20,deg=3)
# Density level set plug-in reconstruction from a sample
# of size 500 (model 8) by using a kernel density
# estimator with uniform kernel
library(DirStats)
f2<-function(x){
set.seed(1)
sample<-rspheremix(500, model = 3)
return(kde_dir(x, data = sample, h = 0.4,
L = function(x) dunif(x)))
}
sphere.hdr(f2,level=0.3)