The Sinepower Covariance Model on the Sphere
RMsinepower is an isotropic covariance model. The
corresponding covariance function, the sine power function of
Soubeyrand, Enjalbert and Sache, only depends on the angle 0 ≤ θ ≤ π between two points on the sphere and is given by
ψ(θ) = 1 - ( sin(θ/2) )^{α},
where 0 < α ≤ 2.
RMsinepower(alpha, var, scale, Aniso, proj)
alpha |
a numerical value in (0,2] |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
For the sine power function of Soubeyrand, Enjalbert and Sache, see
Gneiting, T. (2013), equation (17). For a more general form see RMchoquet.
RMsinepower returns an object of class RMmodel.
Christoph Berreth; Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Gneiting, T. (2013) Strictly and non-strictly positive definite functions on spheres Bernoulli, 19(4), 1327-1349.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again RFoptions(coord_system="sphere") model <- RMsinepower(alpha=1.7) plot(model, dim=2) ## the following two pictures are the same x <- seq(0, 0.4, 0.01) z1 <- RFsimulate(model, x=x, y=x) plot(z1) x2 <- x * 180 / pi z2 <- RFsimulate(model, x=x2, y=x2, coord_system="earth") plot(z2) stopifnot(all.equal(as.array(z1), as.array(z2))) RFoptions(coord_system="auto")
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.