| RMstp {RandomFields} | R Documentation |
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
RMstp(xi, phi, S, z, M, var, scale, Aniso, proj)
xi |
arbitrary univariate function on R^d |
phi |
an |
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 |
See Schlather (2008) formula (13). The model allows for mimicking cyclonic behaviour.
RMstp returns an object of class RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, http://ms.math.uni-mannheim.de
Paciorek C.J., and Schervish, M.J. (2006) Spatial modelling using a new class of nonstationary covariance functions, Environmetrics 17, 483-506.
Schlather, M. (2010) Some covariance models based on normal scale mixtures. Bernoulli, 16, 780-797.
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))