Askey model
Askey's model
C(x)= (1-x)^α 1_{[0,1]}(x)
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
|
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.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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.
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))
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