R: Quasi-arithmetic mean

RMqam {RandomFields} | R Documentation

## 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) = 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` 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.

### 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

`RMqam` returns an object of class `RMmodel`.

### Author(s)

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

### 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

`RMmqam`, `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

    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))

[Package RandomFields version 3.1.50 Index]