qgev.d: 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, ...)

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.

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 $\tau$ (defining flattening of the IDF curve). Default: $\tau=0$.
eta2: numeric value, giving a second duration exponent $\eta_{2}$ (needed for multiscaling). Default: $\eta_2=0$.
...: additional parameters passed to qgev

Details

The duration dependent GEV distribution is defined after [Koutsoyiannis et al., 1998]: $$ G(x)= \exp[-\left( 1+\xi(x/\sigma(d)-\mu_t) \right)^{-1/\xi}] $$ with the duration dependent scale $\sigma(d)=\sigma_0/(d+\theta)^\eta$ and modified location parameter $\mu_t=\mu/\sigma(d)$.

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

Examples

Run this code

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')