RandomFieldsUtils (version 1.2.5)

nonstwm: nonstwm

Description

The non-stationary Whittle-Matern model $C$ is given by

$$C(x,y)=\mathrm{\Gamma }(\mu )\mathrm{\Gamma }(\nu (x){)}^{-1/2}\mathrm{\Gamma }(\nu (y){)}^{-1/2}{W}_{\mu }(f(\mu )|x-y|)$$

where $\mu =[\nu (x)+\nu (y)]/2$, and $\nu$ must a positive function.

$W_{\mu }$ is the covariance function whittle.

The function $f$ takes the following values

scaling = "whittle" :

$f(\mu )=1$

scaling = "matern" :

$f(\mu )=\sqrt{2\nu }$

scaling = "handcockwallis" :

$f(\mu )=2\sqrt{\nu }$

scaling = s, numerical :

$f(\mu )=s\ast \sqrt{nu}$

Usage

nonstwm(x, y, nu, log=FALSE,
        scaling=c("whittle", "matern", "handcockwallis"))

Arguments

x, y

numerical vectors of the same length

nu

positive value or a function with positive values and x as argument

log

logical. If TRUE the logirithm of the covariance function is returned.

scaling

positive value or character; see Details.

Value

A single value is returned.

References

• Stein, M. (2005) Nonstationary Spatial Covariance Functions. Tech. Rep., 2005

See Also

matern.

Examples

# NOT RUN {
nonstwm(2, 1, sin)
# }