Exponential operator
RMexponential yields a covariance model
from a given variogram or covariance model.
The covariance C is given as
C(h) = (\exp(φ(h)) -∑_{k=0}^n φ^k(h)/k!) / (\exp(φ(0)) -∑_{k=0}^n φ^k(0)/k!)
if φ is a covariance model, and as
C(h) = \exp(-φ(h))
if φ is a variogram model.
RMexponential(phi, n, standardised, var, scale, Aniso, proj)
phi |
a valid |
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 |
var,scale,Aniso,proj |
optional arguments; same meaning for any |
If γ is a variogram, then \exp(-γ) is a valid covariance.
RMexponential returns an object of class RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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, Bernoulli 16, 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.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
model <- RMexponential(RMfbm(alpha=1)) ## identical to RMexp()
plot(RMexp(), model=model, type=c("p", "l"), pch=20)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.