RPsmith: (Mixed) Moving Maxima
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Note References See Also Examples

RPsmith defines a moving maximum process or a mixed moving maximum process with finite number of shape functions.

1	RPsmith(shape, tcf, xi, mu, s)

`shape`	an `RMmodel` giving the spectral function
`tcf`	an `RMmodel` specifying the extremal correlation function; either `shape` or `tcf` must be given. If `tcf` is given a shape function is tried to be constructed via the `RMm2r` construction of deterministic, monotone functions.
`xi,mu,s`	the extreme value index, the location parameter and the scale parameter, respectively, of the generalized extreme value distribution. See Details.

\GEV

It simulates max-stable processes Z that are referred to as “Smith model”.

Z(x) = max_{i=1, 2, ...} X_i * Y_i(x - W_i),

where (W_i, X_i) are the points of a Poisson point process on R^d x (0, ∞) with intensity dw * c/x^2 dx and Y_i ~ Y are iid measurable random functions with E[int max(0, Y(x)) dx ] < ∞. The constant c is chosen such that Z has standard Frechet margins.

IMPORTANT: For consistency reasons with the geostatistical definitions in this package the scale argument differs froms the original definition of the Smith model! See the example below.

RPsmith depends on RRrectangular and its arguments.

Advanced options are maxpoints and max_gauss, see RFoptions.

Haan, L. (1984) A spectral representation for max-stable processes. Ann. Probab., 12, 1194-1204.
Smith, R.L. (1990) Max-stable processes and spatial extremes Unpublished Manuscript.

Advanced RMmodels, Auxiliary RMmodels, RMmodel, RPbernoulli, RPgauss, maxstable, maxstableAdvanced.

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RMball()
x <- seq(0, 1000, 0.2)
z <- RFsimulate(RPsmith(model, xi=0), x)
plot(z)
hist(z@data$variable1, 50, freq=FALSE)
curve(exp(-x) * exp(-exp(-x)), from=-3, to=8, add=TRUE)

## 2-dim
x <- seq(0, 10, 0.1) 
z <- RFsimulate(RPsmith(model, xi=0), x, x)
plot(z)

## original Smith model
x <- seq(0, 10, 0.05)
model <- RMgauss(scale = sqrt(2)) # !! cf. definition of RMgauss
z <- RFsimulate(RPsmith(model, xi=0), x, x)
plot(z)




## for some more sophisticated models see 'maxstableAdvanced'