rgparp: Simulation from generalized R-Pareto processes

In mev: Modelling of Extreme Values

Simulation from generalized R-Pareto processes

Description

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))
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')
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')
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))

mev documentation built on Sept. 11, 2024, 8:14 p.m.