RMlsfbm: Locally Positive Definite Function Given by the Fractal...
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Value References See Also Examples

RMlsfbm is a positive definite function on the unit ball in R^d centred at the origin,

C(r) = c - r^α

with 0 <= r = || x - y || <= 1.

1	RMlsfbm(alpha, const, var, scale, Aniso, proj)

alpha

numeric in (0,2); refers to the fractal dimension of the process.

const

the constant c is given by the formula

c = 2^{-α} Γ(d / 2 + α/2) Γ(1 - α/2) / Γ(d / 2)

and should not be changed by the user in order to ensure positive definiteness.

var,scale,Aniso,proj

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

RMlsfbm returns an object of class RMmodel.

Martini, J., Schlather, M., Simianer, H. (In preparation.)

RMbcw generalizes RMlsfbm in case that c is given, RMfbm, RMmodel, RFsimulate, RFfit.

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RMlsfbm(alpha=1, scale=10)
x <- seq(0, 10, 0.02)
plot(model, xlim=c(0,10))
plot(RFsimulate(model, x=x))