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
type4- kappa
shape parameter for
type1,3and4- delta
additional parameter for
type2,3and4- 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.
type0 corresponds to uniform carrier, \(G(u)=u\).type1 corresponds to a three parameters family, with carrier \(G(u)=u^\kappa\).type2 corresponds to a three parameters family, with carrier \(G(u)=1-V_\delta((1-u)^\delta)\).type3 corresponds to a four parameters family, with carrier $$G(u)=1-V_\delta((1-u)^\delta))^{\kappa/2}$$.type4 corresponds to a five parameter model (a mixture oftype2, 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))