R: multivariate quasi-arithmetic mean

RMmqam {RandomFields} | R Documentation

## multivariate quasi-arithmetic mean

### Description

`RMqam` is a multivariate 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_{ij}(h) = φ(√(θ_i (φ^{-1}(C_i(h)))^2 + θ_j (φ^{-1}(C_j(h)))^2 ))

where φ is a completely monotone function, C_i are suitable covariance functions and θ_i≥0 such that ∑_i θ_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 `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.

### 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.

### Value

`RMmqam` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### 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

[Package RandomFields version 3.1.50 Index]