RMstp: Single temporal process

Description Usage Arguments Details Value References See Also Examples

View source: R/RMmodels.R

Description

RMstp is a univariate covariance model which depends on a normal mixture submodel phi. The covariance is given by

C(x,y) = |S_x|^{1/4} |S_y|^{1/4} |A|^{-1/2} φ(Q(x,y)^{1/2})

where

Q(x,y) = c^2 - m^2 + h^t (S_x + 2(m + c)M) A^{-1} (S_y + 2 (m-c)M)h,

c = -z^t h + ξ_2(x) - ξ_2(y),

A = S_x + S_y + 4 M h h^t M

m = h^t M h

h = x - y

Usage

1
RMstp(xi, phi, S, z, M, var, scale, Aniso, proj) 

Arguments

xi

arbitrary univariate function on R^d

phi

an RMmodel that is a normal mixture model, cf.
RFgetModelNames(monotone="normal mixture")

S

functions that returns strictly positive definite d x d

z

arbitrary vector, z \in R^d

M

an arbitrary, symmetric d x d matrix

var,scale,Aniso,proj

optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Details

See Schlather (2008) formula (13). The model allows for mimicking cyclonic behaviour.

Value

RMstp returns an object of class RMmodel.

References

See Also

RMmodel, RFsimulate, RFfit.

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RMstp(xi = RMrotat(phi= -2 * pi, speed=1),
               phi = RMwhittle(nu = 1),
               M=matrix(nc=3, rep(0, 9)),
               S=RMetaxxa(E=rep(1, 3), alpha = -2 * pi,
                          A=t(matrix(nc=3, c(2, 0, 0, 1, 1 , 0, 0, 0, 0))))
              )
x <- seq(0, 10, 0.7)
plot(RFsimulate(model, x=x, y=x, z=x))

RandomFields documentation built on Jan. 19, 2022, 1:06 a.m.