RMqam: Quasi-arithmetic mean

Description

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

C (h) = ϕ (\sqrt{(} \sum_{i} θ_{i} (ϕ^{- 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 that is a normal scale mixture. See, for instance, RFgetModelNames(monotone="normal mixture")

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 arguments; 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 $psi( . ) := phi(sqrt( . ))$ 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.

Examples

Run this code

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RMqam(phi=RMgauss(), RMexp(), RMgauss(),
               theta=c(0.3, 0.7), scale=0.5)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))

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