RandomFields (version 3.0.32)

RMmqam: multivariate quasi-arithmetic mean

Description

RMqam is a multivariate stationary covariance model depending on a submodel $\phi$ such that $\psi(\cdot) := \phi(\sqrt(\cdot))$ is completely monotone, and depending on further stationary covariance models $C_i$. The covariance is given by

$$C_{ij}(h) = \phi(\sqrt(\theta_i (\phi^{-1}(C_i(h)))^2 + \theta_j (\phi^{-1}(C_j(h)))^2 ))$$ where $\phi$ is a completely monotone function, $C_i$ are suitable covariance functions and $\theta_i\ge0$ such that $\sum_i \theta_i=1$.

Usage

RMmqam(phi, C1, C2, C3, C4, C5, C6, C7, C8, C9, theta, var, scale, Aniso, proj)

Arguments

phi

a valid covariance RMmodel that is a normal scale mixture, cf. RFgetModelNames(monotone="normal mixture")

C1, C2, C3, C4, C5, C6, C7, C8, C9

optional further stationary RMmodel

theta

is a vector of values in $[0,1]$, summing up to $1$.

var,scale,Aniso,proj

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

Value

• RMmqam returns an object of class RMmodel

Details

Note that $\psi(\cdot) := \phi(\sqrt(\cdot))$ is completely monotone if and only if $\phi$ is a valid covariance function for all dimensions, e.g. RMstable, RMgauss, RMexponential. Warning: RandomFields cannot check whether the combination of $\phi$ and $C_i$ is valid.

References

• Porcu, E., Mateu, J. & Christakos, G. (2009) Quasi-arithmetic means of covariance functions with potential applications to space-time data.Journal of Multivariate Analysis,100, 1830--1844.

See Also

RMqam, RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
\dontrun{
model <- RMmqam(phi=RMgauss(), RMexp(), RMgauss(), theta=c(0.7, 0.3))
x <- seq(0, 10, if (interactive()) 0.2 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))
}
FinalizeExample()