RandomFields (version 3.0.35)

RMdagum: Dagum Covariance Model Family

Description

RMdagum is a stationary isotropic covariance model. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given by $$C(r) = 1-(1+r^{-\beta})^{\frac{-\gamma}{\beta}}.$$ The parameters $\beta$ and $\gamma$ can be varied in the intervals $(0,1]$ and $(0,1)$, respectively.

Usage

RMdagum(beta, gamma, var, scale, Aniso, proj)

Arguments

beta

numeric in $(0,1]$

gamma

numeric in $(0,1)$

var,scale,Aniso,proj

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

Value

• RMdagum returns an object of class RMmodel

Details

Like the generalized Cauchy model the Dagum family can be used to model fractal dimension and Hurst effect. For a comparison of these see Berg, C. and Mateau, J. and Porcu, E. (2008). This paper also establishes valid parameter choices for the Dagum family, but be careful because therein the model is parameterized differently.

References

• Berg, C. and Mateau, J. and Porcu, E. (2008) The dagum family of isotropic correlation functions.Bernoulli14(4), 1134--1149.

See Also

RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
model <- RMdagum(beta=0.5, gamma=0.5, scale=0.2)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))
FinalizeExample()