RMmqam {RandomFields}

R Documentation

multivariate quasi-arithmetic mean

Description

RMmqam 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. See, for instance, RFgetModelNames(monotone="normal mixture")
C1, C2, C3, C4, C5, C6, C7, C8, C9	optional further stationary RMmodels
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.

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.

Value

RMmqam returns an object of class RMmodel.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

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

RFoptions(modus_operandi="sloppy")
model <- RMmqam(phi=RMgauss(),RMgauss(),RMexp(),theta=c(0.4, 0.6), scale=0.5)
x <- seq(0, 10, 0.02)
plot(model)
z <- RFsimulate(model=model, x=x)
plot(z)

RFoptions(modus_operandi="normal")

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