RMexponential yields a covariance model
from a given variogram or covariance model.
The covariance $C$ of the model is given by
$$C(h) = \frac{\exp(\phi(h)) -\sum_{k=0}^n \phi^k(h)/k!}{\exp(\phi(0))
-\sum_{k=0}^n \phi^k(0)/k!}$$
if $\phi$ is a covariance model.
The covariance $C$ of the model is given by
$$C(h) = \exp(-\phi(h))$$
if $\phi$ is a variogram model.
Usage
RMexponential(phi, n, standardised, var, scale, Aniso, proj)
Arguments
phi
a valid RMmodel; either a variogram model or a
covariance model
n
integer, see formula above. Default is -1.; if the
multivariate dimension of the submodel is greater than 1 then only the
default value is valid.
standardised
logical. If TRUE then the above formula
holds. If FALSE then only the nominator of the above formula is
returned. Default value is TRUE.
var,scale,Aniso,proj
optional parameters; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.
If $\gamma$ is a variogram, then $\exp(-\gamma)$ is a valid
covariance.
References
See, for instance,
Berg, C., Christensen, J. P. R., Ressel, P. (1984)
Harmonic Analysis on Semigroups.Theory of Positive Definite and
Related Functions.Springer, New York.
Sasvari, Z. (2013)Multivariate Characteristic and Correlation
Functions. de Gruyter, Berlin.
Schlather, M. (2010)Some covariance models based on
normal scale mixtures,Bernoulli16, 780-797.
Schlather, M. (2012) Construction of covariance functions and
unconditional simulation of random fields. In
Porcu, E., Montero, J. M., Schlather, M.Advances and Challenges in Space-time Modelling of Natural Events,
Springer, New York.