R: Askey model

RMaskey {RandomFields} | R Documentation

## Askey model

### Description

Askey's model

C(x)= (1-x)^α 1_{[0,1]}(x)

### Usage

    RMaskey(alpha, var, scale, Aniso, proj)
    RMtent(var, scale, Aniso, proj)

### Arguments

`alpha` | a numerical value in the interval [0,1]
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

This covariance function is valid for dimension d if α ≥ (d+1)/2. For α=1 we get the well-known triangle (or tent) model, which is valid on the real line, only.

### Value

`RMaskey` returns an object of class `RMmodel`

### Author(s)

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

### References

Covariance function

- Askey, R. (1973) Radial characteristic functions. Technical report, Research Center, University of Wisconsin-Madison.

- Golubov, B. I. (1981) On Abel-Poisson type and Riesz means, Anal. Math. 7, 161-184.

Applications as covariance function

- Gneiting, T. (1999) Correlation functions for atmospheric data analysis. Quart. J. Roy. Meteor. Soc., 125:2449-2464.

- Gneiting, T. (2002) Compactly supported correlation functions. J. Multivar. Anal., 83:493-508.

- Wendland, H. (1994) Ein Beitrag zur Interpolation mit radialen Basisfunktionen. Diplomarbeit, Goettingen.

- Wendland, H. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. Comput. Math., 4:389-396, 1995.

Tail correlation function (for α ≥ [d / 2] + 1)

- Strokorb, K., Ballani, F., and Schlather, M. (2014) Tail correlation functions of max-stable processes: Construction principles, recovery and diversity of some mixing max-stable processes with identical TCF. Extremes, Submitted.

### See Also

`RMmodel`, `RMbigneiting`, `RMgengneiting`, `RMgneiting`, `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 <- RMtent()
    x <- seq(0, 10, 0.02)
    plot(model)
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]