R: The Sinepower Covariance Model on the Sphere

RMsinepower {RandomFields} | R Documentation

## 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 ≤ 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

`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.

### 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, cberreth@mail.uni-mannheim.de, Martin Schlather

### 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")

[Package RandomFields version 3.1.50 Index]