RandomFields (version 3.0.5)

RMaskey: Askey model

Description

Askey's model $$C(x)= (1-x)^\alpha 1_{[0,1]}(x)$$

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.

Value

• RMaskey returns an object of class RMmodel

Details

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

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 $\alpha \ge [d / 2] + 1$)

• 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, if (interactive()) 0.02 else 1) 
plot(model)
plot(RFsimulate(model, x=x))
FinalizeExample()