RMaskey: Askey model
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

Askey's model

C(x)= (1-x)^α 1_{[0,1]}(x)

1 2	RMaskey(alpha, var, scale, Aniso, proj) RMtent(var, scale, Aniso, proj)

`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.

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 only valid on the real line.

RMaskey returns an object of class RMmodel.

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.

RMmodel, RMbigneiting, RMgengneiting, RMgneiting, RFsimulate, RFfit.

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))