qgev.d: d-GEV quantile function

In IDF: Estimation and Plotting of IDF Curves

d-GEV quantile function

Description

Quantile function of duration-dependent GEV distribution (inverse of the cumulative probability distribution function)

Usage

qgev.d(p, mut, sigma0, xi, theta, eta, d, tau = 0, eta2 = 0, ...)

Arguments

p	vector of probabilities
mut, sigma0, xi	numeric value, giving modified location, modified scale and shape parameter
theta	numeric value, giving duration offset (defining curvature of the IDF curve for short durations)
eta	numeric value, giving duration exponent (defining slope of the IDF curve)
d	positive numeric value, giving duration
tau	numeric value, giving intensity offset τ (defining flattening of the IDF curve). Default: τ=0.
eta2	numeric value, giving a second duration exponent η_{2} (needed for multiscaling). Default: η_2=0.
...	additional parameters passed to qgev

Details

The duration dependent GEV distribution is defined after [Koutsoyiannis et al., 1998]:

G(x)= \exp[-≤ft( 1+ξ(x/σ(d)-μ_t) \right)^{-1/ξ}]

with the duration dependent scale σ(d)=σ_0/(d+θ)^η and modified location parameter μ_t=μ/σ(d).

For details on the d-GEV and the parameter definitions, see IDF-package.

Value

list containing vectors of quantile values for given probabilities. The first element of the list are the q. values for the first given duration etc.

See Also

pgev.d, dgev.d, rgev.d

Examples

p <- c(0.5,0.9,0.99)
# calulate quantiles for one duration
qgev.d(p=p,mut=4,sigma0=2,xi=0,theta=0.1,eta=0.3, d=1)

# calculate quantiles for sequence of durations
ds <- 2^seq(0,4,0.1)
qs <- lapply(ds,qgev.d,p=p,mut=4,sigma0=2,xi=0,theta=0.1,eta=0.3)
qs <- simplify2array(qs)

plot(ds,qs[1,],ylim=c(3,20),type='l',log = 'xy',ylab='Intensity',xlab = 'Duration')
for(i in 2:3){
  lines(ds,qs[i,],lty=i)
}
legend('topright',title = 'p-quantile',
       legend = p,lty=1:3,bty = 'n')

IDF documentation built on July 20, 2022, 5:06 p.m.