R: Exponential operator

RMexponential {RandomFields} | R Documentation

## Exponential operator

### Description

`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.

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

### Details

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

### Value

`RMexponential` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### 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, 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.

### See Also

`RMmodel`, `RFsimulate`, `RFfit`.

### Examples

    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)

[Package RandomFields version 3.1.50 Index]