gamsv: Non-stationary 'centered' semivariogram.

In Jbrich95/sdfExtreme: Spatial Deformation for Non-Stationary Extremal Dependence

Non-stationary 'centered' semivariogram.

Description

Calculates the Fouedijo et al. (2015) theoretical semivariogram. This is a function of some central location o= centre and distance between locations s1 and s2. The semivariogram. has the form

γ^*(s_2,s_1)=γ(||ψ(s_2)-ψ(s_1)||),

where

ψ(s)=o+(s-o)||s-o||

and

γ(x)=(x/λ)^κ

for λ > 0 and κ \in (0,2].

Usage

gamsv(s1, s2, centre = NULL, lam, kap)

Arguments

s1	Vector of length 2 giving coordinates of first location.
s2	Vector of length 2 giving coordinates of second location.
centre	Vector of length 2 giving coordinates of centre of non-stationarity. If NULL, returns stationary semivariogram.
lam	Value of λ.
kap	Value of κ.

Value

Non-stationary semivariogram. between locations s1 and s2

References

Fouedijo et al. (2015) Spatial Statistics, 13:45-61, (doi)

Examples

##Creating correlation values to simulate non-stationary Brown-Resnick process. See help(brnsims).

lambda<-2
centre<-c(0,0)
kappa<-0.8

n.grid<-8
sim.coords<-as.matrix(expand.grid(seq(-1,1,length=n.grid),seq(-1,1,length=n.grid)))

p<-dim(sim.coords)[1]
tau<-matrix(NA,nrow=p,ncol=p)

for(i in 1:p){
for(j in 1:p){
tau[i,j]<-gamsv(s1=sim.coords[i,],s2=c(0,0),lam=lambda,kap=kappa,centre=NULL)+
gamsv(s1=sim.coords[j,],s2=c(0,0),lam=lambda,kap=kappa,centre=NULL)-
gamsv(s1=sim.coords[i,],s2=sim.coords[j,],lam=lambda,kap=kappa,centre=centre)
}
}

##Simulates 10 realisations of non-stationary BR process. 

Sim<-brnsims(reps=10,locs=sim.coords,kappa=kappa,lambda=lambda,centre=centre,tau=tau)

Jbrich95/sdfExtreme documentation built on March 24, 2022, 11:15 a.m.