extgp: Extended generalised Pareto families of Naveau et al. (2016)

In mev: Modelling of Extreme Values

Extended generalised Pareto families of Naveau et al. (2016)

Description

Density function, distribution function, quantile function and random generation for the extended generalized Pareto distribution (GPD) with scale and shape parameters.

Arguments

q	vector of quantiles
x	vector of observations
p	vector of probabilities
n	sample size
prob	mixture probability for model type 4
kappa	shape parameter for type 1, 3 and 4
delta	additional parameter for type 2, 3 and 4
sigma	scale parameter
xi	shape parameter
type	integer between 0 to 5 giving the model choice
step	function of step size for discretization with default 0, corresponding to continuous quantiles
log	logical; should the log-density be returned (default to FALSE)?
unifsamp	sample of uniform; if provided, the data will be used in place of new uniform random variates
censoring	numeric vector of length 2 containing the lower and upper bound for censoring

Details

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

Usage

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))

Author(s)

Raphael Huser and Philippe Naveau

References

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.

mev documentation built on April 20, 2023, 5:10 p.m.