Cox Isham Covariance Model
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) between two points in d+1-dimensional space and is given by
C(h,t)=|E + t^β D|^{-1/2} C_0([(h - t μ)^T (E + t^β D)^{-1} (h - t μ)]^{1/2})
Here μ is a vector in d-dimensional space; E is the d x d-identity matrix and D is a d x d-correlation matrix with |D| > 0. The parameter β is in (0,2]. Currently, the implementation is done only for d=2.
RMcoxisham(phi,mu,D,beta,var, scale, Aniso, proj)
phi |
a univariate stationary isotropic covariance model for random fields
on d-dimensional space, which is moreover a normal scale
mixture, that means an
|
mu |
a vector in d-dimensional space |
D |
a d x d-correlation matrix with |D| > 0 |
beta |
numeric in the interval (0,2]; default value is 2 |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
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. Schlather, M. (2010), Example 9).
RMcoxisham returns an object of class RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again model <- RMcoxisham(RMgauss(), mu=1, D=1) x <- seq(0, 10, 0.3) plot(model, dim=2) plot(RFsimulate(model, x=x, y=x))
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.