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
- riskf
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.
- weights
vector of length
mfor themmixture components. Must sum to one- vario
semivariogram function whose first argument must be distance. Used only if provided in conjunction with
coordand ifsigmais missing- coord
dbykmatrix of coordinates, used as input in the variogramvarioor as parameter for the Smith model. IfgridisTRUE, 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, riskf = '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, riskf = '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,] 0.0006178841 0.001685128 9.29815316 0.001798982
#> [2,] 1.0336443059 1.638952959 3.82220506 2.824784843
#> [3,] 0.3463753792 0.436664009 0.12161582 1.658228783
#> [4,] 0.3681898038 1.003803544 0.76459068 1.177343941
#> [5,] 1.6591443934 2.141095273 0.65556079 3.003799661
#> [6,] 0.4147096140 1.076215146 0.23639320 1.739773536
#> [7,] 1.0603637236 1.990356848 0.40652762 3.699056361
#> [8,] 0.1246372190 0.235534601 0.08492149 2.333862118
#> [9,] 7.4561392330 18.642215340 73.04767832 20.004289236
#> [10,] 0.5584019012 1.492700141 1.76092295 1.870341412
#> attr(,"accept.rate")
#> [1] 0.4137931
rgparp(n = 10, riskf = '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,] 4.790862312 0.01032648 2.193012e-03
#> [2,] 0.009859696 0.03745091 9.635744e+00
#> [3,] 12.936481605 6.14352004 1.363821e+00
#> [4,] 0.181337733 0.39745850 3.721127e+01
#> [5,] 2.200792027 0.92473635 1.869372e+00
#> [6,] 0.751530870 4.18018890 9.843943e-01
#> [7,] 3.780335206 6.37163408 1.434532e+00
#> [8,] 8.192618544 39.18135029 4.893656e+00
#> [9,] 0.672241559 1.55617823 1.114769e+02
#> [10,] 13.863862463 31.72293440 1.456349e+01
#> 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, riskf = 'max', vario = vario, coord = grid.coord,
model = 'br', scale = runif(16), loc = rnorm(16))
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0.8131132 -1.0201245 -1.012336 0.1289821 -1.093509 1.0347484 0.3934998
#> [2,] 0.8128315 -1.0376203 -1.012814 0.1291347 -1.092575 0.9520569 0.3810090
#> [3,] 0.8125650 -0.9786162 -1.028973 0.1306269 -1.096913 1.0835454 0.3898558
#> [4,] 0.8120891 -0.9782802 -1.021704 0.1303578 -1.124843 1.0671353 0.3773491
#> [5,] 0.8131356 -1.0098537 -1.011041 0.1300492 -1.101756 0.9928481 0.3855674
#> [6,] 0.8129728 -1.0376149 -1.008736 0.1293803 -1.100383 0.9897208 0.3792453
#> [7,] 0.8125853 -0.9781316 -1.011748 0.1301468 -1.093596 1.0741062 0.3786765
#> [8,] 0.8129230 -0.9639166 -1.008473 0.1306683 -1.124330 1.0782159 0.3794997
#> [9,] 0.8134280 -1.0385922 -1.001636 0.1288303 -1.083310 1.0922922 0.3945636
#> [10,] 0.8130283 -0.9812439 -1.009823 0.1305610 -1.091652 1.0837451 0.3882692
#> [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] -0.9518330 -1.232997 -2.902765 -2.025643 -1.833081 0.6723882 1.138928
#> [2,] -0.9984800 -1.238813 -2.943585 -2.053805 -1.843602 0.6400419 1.111419
#> [3,] -0.9294300 -1.260937 -2.880665 -2.092224 -1.802201 0.6952242 1.131607
#> [4,] -0.9335313 -1.258497 -2.900660 -2.072263 -1.823244 0.6805283 1.132111
#> [5,] -0.9967743 -1.238425 -2.920725 -2.030700 -1.823680 0.5223860 1.118087
#> [6,] -1.0134395 -1.235314 -2.919007 -2.023749 -1.836525 0.6168533 1.113628
#> [7,] -0.9177161 -1.254359 -2.900054 -2.034860 -1.824908 0.6938025 1.139935
#> [8,] -0.9225261 -1.236694 -2.871461 -2.014178 -1.795755 0.6396206 1.135119
#> [9,] -0.9192352 -1.224811 -2.949016 -2.003990 -1.852326 0.7031268 1.142410
#> [10,] -0.9331708 -1.236176 -2.878832 -2.038804 -1.803844 0.6950481 1.137635
#> [,15] [,16]
#> [1,] -1.172673 1.235146
#> [2,] -1.245759 1.174119
#> [3,] -1.159101 1.226116
#> [4,] -1.172936 1.227901
#> [5,] -1.325217 1.164613
#> [6,] -1.285469 1.128961
#> [7,] -1.167054 1.242987
#> [8,] -1.281553 1.235689
#> [9,] -1.140690 1.237267
#> [10,] -1.159233 1.234506
#> attr(,"accept.rate")
#> [1] 1