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 $0 \le \theta \le \pi$ between two points on the sphere and is given by

ψ (θ) = 1 - (s i n \frac{θ}{2})^{α}

where $0 < \alpha \le 2$.

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.

Examples

Run this code

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")

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