nonstwm {RandomFieldsUtils}

R Documentation

nonstwm

Description

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

C(x, y)=\Gamma(\mu) \Gamma(\nu(x))^{-1/2} \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 * \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.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

References

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

See Also

matern.

Examples

nonstwm(2, 1, sin)

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