RMcoxisham: Cox Isham Covariance Model
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

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.

1	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 `RMmodel` whose `monotone` property equals `'normal mixture'`, see `RFgetModelNames(monotone="normal mixture")` and whose `maxdim` is at least 2.
`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 `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. Schlather, M. (2010), Example 9).

RMcoxisham returns an object of class RMmodel.

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.

RMmodel, RFsimulate, RFfit.

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))

Loading required package: sp
Loading required package: RandomFieldsUtils

Attaching package: 'RandomFields'

The following object is masked from 'package:RandomFieldsUtils':

    RFoptions

The following objects are masked from 'package:base':

    abs, acosh, asin, asinh, atan, atan2, atanh, cos, cosh, exp, expm1,
    floor, gamma, lgamma, log, log1p, log2, logb, max, min, round, sin,
    sinh, sqrt, tan, tanh, trunc

NULL
NOTE: simulation is performed with fixed random seed 0.
Set 'RFoptions(seed=NA)' to make the seed arbitrary.
New output format of RFsimulate: S4 object of class 'RFsp';
for a bare, but faster array format use 'RFoptions(spConform=FALSE)'.