RMcoxisham is a stationary covariance model
which depends on a univariate stationary isotropic covariance model
$C_0$, which is a normal scale mixture.
The corresponding covariance function only depends on the difference
$(h,t) \in {\bf R}^{d+1}={\bf R}^d\times{\bf R}$ between two points in $d+1$-dimensional space and is given by
$$C(h,t)=|E + t^\beta D|^{-1/2} C_0([(h - t \mu)^T (E + t^\beta
D)^{-1} (h - t \mu)]^{1/2})$$
Here $\mu \in {\bf R}^d$ is a vector in
$d$-dimensional space;
$E$ is the $d \times d$-identity matrix and $D$ is
a $d \times d$-correlation matrix with $|D| > 0$.
The parameter $\beta$ is in $(0,2]$.
Currently, the implementation is done only for $d=2$.
Usage
RMcoxisham(phi,mu,D,beta,var, scale, Aniso, proj)
Arguments
phi
a univariate stationary isotropic covariance model for random fields
on $d$-dimensional space, which is moreover a normal scale
mixture, that means an
RMmodel whose normalmix equals
T
mu
a vector in $d$-dimensional space
D
a $d \times d$-correlation matrix with $|D| >
0$
beta
a parameter in the interval $(0,2]$, default value is 2
var,scale,Aniso,proj
optional parameters; same meaning for any
RMmodel. If not passed, the above
covariance function remains unmodified.
This model stems from a rainfall model (cf. Cox, D.R., Isham,
V.S. (1988)) and equals the following expectation
$$C(h,t)=\bold{E}_V C_0(h-Vt)$$
where the random wind speed vector $V$ follows a $d$-variate
normal distribution with expectation $mu$ and covariance matrix $D/2$.
(cf. See Schlather, M. (2010), Example 9).
References
Cox, D.R., Isham, V.S. (1988)
A simple spatial-temporal model of rainfall.Proc. R. Soc. Lond. A,415, 317-328.
Schlather, M. (2010)
On some covariance models based on normal scale mixtures.Bernoulli,16, 780-797.