nonstwm

nonstwm

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 :

\(f(\mu) = s * \sqrt{nu}\)

Keywords
models, spatial
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.

For more details see RMnonstwm.

Aliases
  • nonstwm
Examples
# NOT RUN {
nonstwm(2, 1, sin)
# }
Documentation reproduced from package RandomFieldsUtils, version 0.5.3, License: GPL (>= 3)

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