Density function, distribution function, quantile function and random generation for the extended generalized Pareto distribution (GPD) with scale and shape parameters.
vector of quantiles
vector of observations
vector of probabilities
sample size
mixture probability for model type 4
shape parameter for type 1, 3 and 4
additional parameter for type 2, 3 and 4
scale parameter
shape parameter
integer between 0 to 5 giving the model choice
function of step size for discretization with default 0, corresponding to continuous quantiles
logical; should the log-density be returned (default to FALSE)?
sample of uniform; if provided, the data will be used in place of new uniform random variates
numeric vector of length 2 containing the lower and upper bound for censoring
pextgp(q, prob=NA, kappa=NA, delta=NA, sigma=NA, xi=NA, type=1)
dextgp(x, prob=NA, kappa=NA, delta=NA, sigma=NA, xi=NA, type=1, log=FALSE)
qextgp(p, prob=NA, kappa=NA, delta=NA, sigma=NA, xi=NA, type=1)
rextgp(n, prob=NA, kappa=NA, delta=NA, sigma=NA, xi=NA, type=1, unifsamp=NULL, censoring=c(0,Inf))
Raphael Huser and Philippe Naveau
The extended generalized Pareto families proposed in Naveau et al. (2016) retain the tail index of the distribution while being compliant with the theoretical behavior of extreme low rainfall. There are five proposals, the first one being equivalent to the GP distribution.
type 0 corresponds to uniform carrier, \(G(u)=u\).
type 1 corresponds to a three parameters family, with carrier \(G(u)=u^\kappa\).
type 2 corresponds to a three parameters family, with carrier \(G(u)=1-V_\delta((1-u)^\delta)\).
type 3 corresponds to a four parameters family, with carrier $$G(u)=1-V_\delta((1-u)^\delta))^{\kappa/2}$$.
type 4 corresponds to a five parameter model (a mixture of type 2, with \(G(u)=pu^\kappa + (1-p)*u^\delta\)
Naveau, P., R. Huser, P. Ribereau, and A. Hannart (2016), Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection, Water Resour. Res., 52, 2753-2769, doi:10.1002/2015WR018552.