RandomFields (version 3.1.12)

RMsinepower: The Sinepower Covariance Model on the Sphere

Description

RMsinepower is a isotropic covariance model. The corresponding covariance function, the sine power function of Soubeyrand, Enjalbert and Sache, only depends on the angle $\theta \in [0,\pi]$ between two points on the sphere and is given by $$\psi(\theta) = 1 - ( sin\frac{\theta}{2} )^{\alpha}$$ where $\alpha\in (0,2]$.

Usage

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

Arguments

alpha

a numerical value in $(0,2]$

var,scale,Aniso,proj

optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Value

• RMsinepower returns an object of class RMmodel

Details

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

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
StartExample()

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")
FinalizeExample()