rmpareto_tree {graphicalExtremes} | R Documentation |
Sampling of a multivariate Pareto distribution on a tree
Description
Simulates exact samples of a multivariate Pareto distribution that is an extremal graphical model on a tree as defined in Engelke and Hitz (2020).
Usage
rmpareto_tree(n, model = c("HR", "logistic", "dirichlet")[1], tree, par)
Arguments
n |
Number of simulations. |
model |
The parametric model type; one of:
|
tree |
Graph object from |
par |
Respective parameter for the given
|
Details
The simulation follows the algorithm in Engelke and Hitz (2020). 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).
Value
Numeric matrix of simulations of the
multivariate Pareto distribution.
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.
Engelke S, Hitz AS (2020).
“Graphical models for extremes (with discussion).”
J. R. Stat. Soc. Ser. B Stat. Methodol., 82, 871–932.
See Also
Other sampling functions:
rmpareto()
,
rmstable_tree()
,
rmstable()
Examples
## A 4-dimensional HR tree model
my_tree <- igraph::graph_from_adjacency_matrix(rbind(
c(0, 1, 0, 0),
c(1, 0, 1, 1),
c(0, 1, 0, 0),
c(0, 1, 0, 0)
),
mode = "undirected"
)
n <- 10
Gamma_vec <- c(.5, 1.4, .8)
set.seed(123)
rmpareto_tree(n, "HR", tree = my_tree, par = Gamma_vec)
## A 4-dimensional Dirichlet model with asymmetric edge distributions
alpha <- cbind(c(.2, 1, .5), c(1.5, .6, .8))
rmpareto_tree(n, model = "dirichlet", tree = my_tree, par = alpha)