RMexponential: Exponential operator
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

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.

1	RMexponential(phi, n, standardised, var, scale, Aniso, proj)

`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 arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

If γ is a variogram, then \exp(-γ) is a valid covariance.

RMexponential returns an object of class RMmodel.

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.

RMmodel, RFsimulate, RFfit.

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)