RandomFields (version 3.0.10)

RMqam: Quasi-arithmetic mean

Description

RMqam is a univariate 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 $$C(h) = \phi(\sqrt(\sum_i \theta_i (\phi^{-1}(C_i(h)))^2))$$

Usage

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

Arguments

phi

a valid covariance RMmodel where normalmix is true

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

optional further univariate stationary RMmodel.

theta

a vector with positive entries

var,scale,Aniso,proj

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

Value

• RMqam 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. (2007) Quasi-arithmetic means of covariance functions with potential applications to space-time data. Submitted to Journal of Multivariate Analysis.

See Also

RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0)
\dontrun{
model <- RMqam(phi=RMgauss(), RMexp(), RMgauss(),
               theta=c(0.3, 0.7), scale=0.5)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))
}
RFoptions(seed=NA)