RMlgd: Local-Global Distinguisher Family Covariance Model

Description

RMlgd is a stationary isotropic covariance model, which is valid only for dimensions $d =1,2$. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given by

C (r) = 1 - β^{- 1} (α + β) r^{α} 1_{[0, 1]} (r) + α^{- 1} (α + β) r^{- β} 1_{r > 1} (r)

where $\beta >0$ and $0 < \alpha \le (3-d)/2$, with $d$ denoting the dimension of the random field.

Usage

RMlgd(alpha, beta, var, scale, Aniso, proj)

Arguments

alpha

parameter whose range is dependend on the dimension of the random field: $0< \alpha \le (3-d)/2$.

beta

beta > 0.

var,scale,Aniso,proj

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

Value

RMlgd returns an object of class RMmodel

Details

The model is only valid for dimension $d=1,2$.

This model admits simulating random fields where RFfractaldimension D of the Gaussian sample and Hurst coefficient H can be chosen independently (compare also RMgencauchy.):

Here, the random field has RFfractaldimension $D = d + 1 - α / 2$ and Hurst coefficient $H = 1 - β / 2$ for $0< \beta \le 1$.

References

Gneiting, T. and Schlather, M. (2004) Stochastic models which separate RFfractaldimension and Hurst effect.SIAM review46, 269--282.

Examples

Run this code

set.seed(0)
model <- RMlgd(alpha=0.7, beta=4, scale=0.5)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))

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