RMmultiquad
is a isotropic covariance model. The
corresponding covariance function, the multiquadric family, only
depends on the angle 0 ≤ θ ≤ π
between two points on the sphere and is given by
ψ(θ) = (1  δ)^{2*τ} / (1 + delta^2  2*δ*cos(θ))^{τ},
where 0 < δ < 1 and τ > 0.
1  RMmultiquad(delta, tau, var, scale, Aniso, proj)

delta 
a numerical value in (0,1) 
tau 
a numerical value greater than 0 
var,scale,Aniso,proj 
optional arguments; same meaning for any

Special cases (cf. Gneiting, T. (2013), p.1333) are known for fixed parameter τ=0.5 which leads to the covariance function called 'inverse multiquadric'
ψ(θ) = (1  δ) / √( 1 + delta^2  2*δ*cos(θ) )
and for fixed parameter τ=1.5 which gives the covariance function called 'Poisson spline'
ψ(θ) = (1  δ)^{3} / (1 + delta^2  2*δ*cos(θ))^{1.5}.
For a more general form, see RMchoquet
.
RMmultiquad
returns an object of class RMmodel
Christoph Berreth, cberreth@mail.unimannheim.de, Martin Schlather
Gneiting, T. (2013) Strictly and nonstrictly positive definite functions on spheres Bernoulli, 19(4), 13271349.
RMmodel
,
RFsimulate
,
RFfit
,
RMchoquet
,
spherical models
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  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 < RMmultiquad(delta=0.5, tau=1)
plot(model, dim=2)
## the following two pictures are the same
x < seq(0, 0.12, 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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