The Sinepower Covariance Model on the Sphere

Description

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.

Usage

RMsinepower(alpha, var, scale, Aniso, proj)

Arguments

Details

For the sine power function of Soubeyrand, Enjalbert and Sache, see Gneiting, T. (2013), equation (17). For a more general form see RMchoquet.

Value

RMsinepower returns an object of class RMmodel.

Author(s)

Christoph Berreth; Martin Schlather, schlather@math.uni-mannheim.de, http://ms.math.uni-mannheim.de

References

Gneiting, T. (2013) Strictly and non-strictly positive definite functions on spheres Bernoulli, 19(4), 1327-1349.

See Also

RMmodel, RFsimulate, RFfit, spherical models, RMchoquet

Examples

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")