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).
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 - mfor the- mmixture components that sum to one. For the- "maxlin"model, weights should be a matrix with- dcolumns 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 - coordand if- sigmais missing
- coord
- dby- kmatrix of coordinates, used as input in the variogram- varioor as parameter for the Smith model. If- gridis- TRUE, unique entries should be supplied.
- ...
- additional arguments for the - variofunction
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