Description

RMstable is a stationary isotropic covariance model belonging to the so called stable family. The corresponding covariance function only depends on the distance r ≥ 0 between two points and is given by

C(r)=e^{-r^α}

where 0 < α ≤ 2.

Usage

Arguments

Details

The parameter α determines the fractal dimension D of the Gaussian sample paths:

D = d + 1 - α/2

where d is the dimension of the random field. For α < 2 the Gaussian sample paths are not differentiable (cf. Gelfand et al., 2010, p. 25).

Each covariance function of the stable family is a normal scale mixture.

The stable family includes the exponential model (see RMexp) for α = 1 and the Gaussian model (see RMgauss) for α = 2.

The model is called stable, because in the 1-dimensional case the covariance is the characteristic function of a stable random variable (cf. Chiles, J.-P. and Delfiner, P. (1999), p. 90).

Value

RMstable returns an object of class RMmodel.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

References

Covariance function

• Chiles, J.-P. and Delfiner, P. (1999) Geostatistics. Modeling Spatial Uncertainty. New York: Wiley.

• Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998) Model-based geostatistics (with discussion). Applied Statistics 47, 299–350.

• Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp, P. (eds.) (2010) Handbook of Spatial Statistics. Boca Raton: Chapman & Hall/CRL.

Tail correlation function (for 0 < α ≤ 1)

• Strokorb, K., Ballani, F., and Schlather, M. (2014) Tail correlation functions of max-stable processes: Construction principles, recovery and diversity of some mixing max-stable processes with identical TCF. Extremes, Submitted.

See Also

RMbistable, RMexp, RMgauss, RMmodel, RFsimulate, RFfit.

Examples