Simulation from generalized R-Pareto processes

The generalized R-Pareto process is supported on (loc - scale / shape, Inf) if shape > 0, or (-Inf, loc - scale / shape) for negative shape parameters, conditional on \((X-r(loc))/r(scale)>0\). The standard Pareto process corresponds to scale = loc = rep(1, d).

Usage

rgparp(
  n,
  shape = 1,
  thresh = 1,
  risk = c("mean", "sum", "site", "max", "min", "l2"),
  siteindex = NULL,
  d,
  loc,
  scale,
  param,
  sigma,
  model = c("log", "neglog", "bilog", "negbilog", "hr", "br", "xstud", "smith",
    "schlather", "ct", "sdir", "dirmix"),
  weights,
  vario,
  coord = NULL,
  ...
)

Arguments

n: number of observations
shape: shape parameter of the generalized Pareto variable
thresh: univariate threshold for the exceedances of risk functional
risk: string indicating the risk functional.
siteindex: integer between 1 and d specifying the index of the site or variable
d: dimension of sample
loc: location vector
scale: scale vector
param: parameter vector for the logistic, bilogistic, negative bilogistic and extremal Dirichlet (Coles and Tawn) model. Parameter matrix for the Dirichlet mixture. Degree of freedoms for extremal student model. See Details.
sigma: covariance matrix for Brown-Resnick and extremal Student-t distributions. Symmetric matrix of squared coefficients \(\lambda^2\) for the Husler-Reiss model, with zero diagonal elements.
model: for multivariate extreme value distributions, users can choose between 1-parameter logistic and negative logistic, asymmetric logistic and negative logistic, bilogistic, Husler-Reiss, extremal Dirichlet model (Coles and Tawn) or the Dirichlet mixture. Spatial models include the Brown-Resnick, Smith, Schlather and extremal Student max-stable processes. Max linear models are also supported
weights: vector of length m for the m mixture components that sum to one. For the "maxlin" model, weights should be a matrix with d columns that represent the weight of the components and whose column sum to one (if provided, this argument overrides asy).
vario: semivariogram function whose first argument must be distance. Used only if provided in conjunction with coord and if sigma is missing
coord: d by k matrix of coordinates, used as input in the variogram vario or as parameter for the Smith model. If grid is TRUE, unique entries should be supplied.
...: additional arguments for the vario function

Value

an n by d sample from the generalized R-Pareto process, with attributes accept.rate if the procedure uses rejection sampling.

Examples

rgparp(n = 10, risk = 'site', siteindex = 2, d = 3, param = 2.5,
   model = 'log', scale = c(1, 2, 3), loc = c(2, 3, 4))
#> Warning: longer object length is not a multiple of shorter object length
#>       [,1] [,2] [,3]
#>  [1,]    1    1    1
#>  [2,]    1    1    1
#>  [3,]    1    1    1
#>  [4,]    1    1    1
#>  [5,]    1    1    1
#>  [6,]    1    1    1
#>  [7,]    1    1    1
#>  [8,]    1    1    1
#>  [9,]    1    1    1
#> [10,]    1    1    1
#> attr(,"accept.rate")
#> [1] 1
rgparp(n = 10, risk = 'max', d = 4, param = c(0.2, 0.1, 0.9, 0.5),
   scale = 1:4, loc = 1:4, model = 'bilog')
#>             [,1]       [,2]      [,3]      [,4]
#>  [1,] 0.16708294 0.84822858 0.0972277 1.5847869
#>  [2,] 0.54178861 1.06026266 0.3278755 0.9523174
#>  [3,] 0.18320648 0.41630489 0.0415351 1.3124610
#>  [4,] 0.51300988 1.22361722 0.3163796 1.5027287
#>  [5,] 0.04647777 0.08431727 0.1096085 1.2651984
#>  [6,] 0.46184319 1.09822713 0.5917206 3.6846269
#>  [7,] 0.55111207 1.14657949 0.1599802 1.9248288
#>  [8,] 0.38445423 0.81078795 4.2529464 6.2350637
#>  [9,] 0.20722129 0.39159880 0.1411901 3.8802689
#> [10,] 0.97773079 2.61363525 3.0832785 3.2748642
#> attr(,"accept.rate")
#> [1] 0.425
rgparp(n = 10, risk = 'sum', d = 3, param = c(0.8, 1.2, 0.6, -0.5),
   scale = 1:3, loc = 1:3, model = 'sdir')
#>               [,1]         [,2]       [,3]
#>  [1,]  1.910703289 10.227383209  0.6664815
#>  [2,]  1.905321208  3.949975171 69.5366495
#>  [3,]  2.944172088  0.953649788  0.4577316
#>  [4,] 56.665476826  7.542547592  4.6172216
#>  [5,]  4.929917270  2.036208724  1.2816897
#>  [6,]  2.478666942  7.245128077  3.7793809
#>  [7,]  0.411258103  1.163707773  6.3278698
#>  [8,]  0.006839741  0.006774305  9.4990915
#>  [9,]  1.914708100  1.501158342  1.5245586
#> [10,]  1.623081281 13.729665409 81.0419152
#> attr(,"accept.rate")
#> [1] 1
vario <- function(x, scale = 0.5, alpha = 0.8){ scale*x^alpha }
grid.coord <- as.matrix(expand.grid(runif(4), runif(4)))
rgparp(n = 10, risk = 'max', vario = vario, coord = grid.coord,
   model = 'br', scale = runif(16), loc = rnorm(16))
#>            [,1]       [,2]        [,3]        [,4]      [,5]       [,6]
#>  [1,] -2.975997  -1.649098 -0.04782119   0.2163726 -1.767358  -2.218900
#>  [2,] -3.076005  -2.925881 -1.56208458  -0.6447922 -1.808855  -2.463810
#>  [3,] -3.285106  -5.170135 -0.96529235   0.5759286 -2.016755  -8.286711
#>  [4,] -3.252408  -3.266976 -1.41537414   0.5996892 -1.865884  -3.433610
#>  [5,] -3.040683  -2.794275  0.15429560   0.9437330 -1.824155  -2.582566
#>  [6,] -2.954477  -2.024722 -0.74602130  -0.1377545 -1.739974  -1.344229
#>  [7,] -3.109310  -2.954373 -0.32241898   0.7182453 -1.895561  -4.378893
#>  [8,] -4.034499 -18.774690 -6.09310721 -17.6278359 -2.099146 -10.111957
#>  [9,] -3.311906  -7.183397 -2.52191152  -6.7623727 -2.001773  -9.268944
#> [10,] -3.174855  -3.579029 -0.62510775   0.2277307 -1.800448  -2.787185
#>             [,7]       [,8]      [,9]      [,10]     [,11]       [,12]    [,13]
#>  [1,] -0.9132273  -2.464539 -1.591269  -2.900593 -0.812110  -1.4943176 1.619361
#>  [2,] -2.3498990  -2.604959 -2.765860  -4.375954 -1.687790  -1.9135135 1.581973
#>  [3,] -2.2226005  -1.842195 -4.872853 -12.416238 -1.488860  -1.2938327 1.485450
#>  [4,] -2.3317053  -1.802833 -2.894217  -4.476507 -1.137947  -1.5833872 1.597314
#>  [5,] -0.8666341  -1.688941 -2.074563  -3.514826 -0.763012  -0.6999166 1.591352
#>  [6,] -1.3026493  -2.353987 -1.102975  -2.216203 -1.439773  -1.9943447 1.631801
#>  [7,] -2.0947424  -1.597832 -4.205934  -7.784464 -1.601200  -0.6118442 1.567423
#>  [8,] -8.0705527 -19.736783 -8.068216 -19.135874 -4.707461 -27.3795501 1.350833
#>  [9,] -2.0534034  -6.772165 -4.326546  -7.708982 -1.894134  -6.1014218 1.507648
#> [10,] -1.5609782  -2.349590 -2.554410  -5.480664 -1.214084  -1.4781656 1.598181
#>           [,14]       [,15]     [,16]
#>  [1,] -1.101950 -0.18766566 -3.565759
#>  [2,] -1.320125 -1.86742032 -3.750749
#>  [3,] -3.345406 -0.96832255 -3.496404
#>  [4,] -1.540604 -1.74731883 -3.508608
#>  [5,] -1.481214 -0.03431142 -3.379791
#>  [6,] -1.047704 -0.78664121 -3.615796
#>  [7,] -1.656449 -1.59121166 -3.417975
#>  [8,] -3.821685 -7.25720535 -6.494530
#>  [9,] -2.660784 -1.94550797 -4.279763
#> [10,] -1.297163 -0.62875180 -3.571205
#> attr(,"accept.rate")
#> [1] 0.7857143