Simulates exact samples of a multivariate max-stable distribution.
Usage
rmstable(n, model = c("HR", "logistic", "neglogistic", "dirichlet")[1], d, par)Arguments
- n
Number of simulations.
- model
The parametric model type; one of:
HR(default),logistic,neglogistic,dirichlet.
- d
Dimension of the multivariate Pareto distribution.
- par
Respective parameter for the given
model, that is,\(\Gamma\), numeric \(d \times d\) variogram matrix, if
model = HR.\(\theta \in (0, 1)\), if
model = logistic.\(\theta > 0\), if
model = neglogistic.\(\alpha\), numeric vector of size
dwith positive entries, ifmodel = dirichlet.
Details
The simulation follows the extremal function algorithm in Dombry et al. (2016) . For details on the parameters of the Huesler-Reiss, logistic and negative logistic distributions see Dombry et al. (2016) , and for the Dirichlet distribution see Coles and Tawn (1991) .
References
Coles S, Tawn JA (1991).
“Modelling extreme multivariate events.”
J. R. Stat. Soc. Ser. B Stat. Methodol., 53, 377--392.
Dombry C, Engelke S, Oesting M (2016).
“Exact simulation of max-stable processes.”
Biometrika, 103, 303--317.
See also
Other sampling functions:
rmpareto(),
rmpareto_tree(),
rmstable_tree()
Examples
## A 4-dimensional HR distribution
n <- 10
d <- 4
G <- cbind(
c(0, 1.5, 1.5, 2),
c(1.5, 0, 2, 1.5),
c(1.5, 2, 0, 1.5),
c(2, 1.5, 1.5, 0)
)
rmstable(n, "HR", d = d, par = G)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.9129700 2.7320869 4.3930684 2.0396394
#> [2,] 0.2666331 0.7563013 1.6998662 0.7642649
#> [3,] 1.4469430 3.2588614 0.6616103 0.9099434
#> [4,] 0.4459274 1.6260210 0.6936030 1.0758879
#> [5,] 0.4388372 0.7088128 0.4051627 0.5354991
#> [6,] 0.5635592 0.6925003 2.5880064 0.4623138
#> [7,] 1.6316665 1.2772479 2.3119953 6.8583689
#> [8,] 25.5877634 9.4518333 30.2610583 11.8954021
#> [9,] 9.1793281 9.6263068 7.7595231 18.7535580
#> [10,] 23.4589286 30.4513683 27.9736059 12.6065325
## A 3-dimensional logistic distribution
n <- 10
d <- 3
theta <- .6
rmstable(n, "logistic", d, par = theta)
#> [,1] [,2] [,3]
#> [1,] 0.7920967 0.3838593 0.5446596
#> [2,] 0.4762412 1.7332709 1.3834479
#> [3,] 1.3370597 0.2851836 4.0607764
#> [4,] 0.7421880 1.8327530 2.2199731
#> [5,] 1.9280030 10.7751455 1.5144490
#> [6,] 1.2808886 0.8044145 0.8670885
#> [7,] 1.2840544 0.7799514 5.0934757
#> [8,] 0.5676049 0.3633312 0.3426581
#> [9,] 0.2693890 0.3870772 0.4698337
#> [10,] 1.0291076 0.4829797 1.6501069
## A 5-dimensional negative logistic distribution
n <- 10
d <- 5
theta <- 1.5
rmstable(n, "neglogistic", d, par = theta)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 7.6648654 12.7130188 5.1404650 29.9312790 6.7218769
#> [2,] 0.6997510 0.7048263 1.2611360 0.8094214 0.5227736
#> [3,] 23.7136939 1.8638248 7.7195594 8.6375029 18.3126055
#> [4,] 1.1596061 0.9826885 1.1413147 1.3009600 0.4160243
#> [5,] 1.3697433 0.6338478 0.7218860 1.4924707 0.9762449
#> [6,] 2.2482129 2.8355838 1.4315486 4.9443567 1.6710074
#> [7,] 16.7420023 15.0632920 12.9267446 20.3789551 28.2010827
#> [8,] 0.4362455 0.3568023 0.3109209 0.9655873 0.3155885
#> [9,] 0.8675428 0.6111543 0.4107973 0.8449127 0.6456791
#> [10,] 3.8236338 3.0036666 4.5845912 1.6076321 2.4079347
## A 4-dimensional Dirichlet distribution
n <- 10
d <- 4
alpha <- c(.8, 1, .5, 2)
rmstable(n, "dirichlet", d, par = alpha)
#> [,1] [,2] [,3] [,4]
#> [1,] 1.8895508 0.7655561 1.2157059 2.1661873
#> [2,] 0.7099777 1.8470676 3.6166997 0.7038762
#> [3,] 3.0723931 0.4386526 0.9849517 0.7825669
#> [4,] 0.5039515 0.4160592 0.9417922 2.8132326
#> [5,] 8.8648594 2.9460901 7.5495707 6.8022550
#> [6,] 2.8973698 4.9357845 2.1741180 4.9137229
#> [7,] 1.5847216 6.1903019 3.3346973 1.8198441
#> [8,] 0.2975653 1.2948784 1.5564330 2.1926874
#> [9,] 1.3155831 0.5673063 0.4437899 1.0480459
#> [10,] 1.7603035 5.4723088 1.5448006 4.8258270