qgev.d {IDF}

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 \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.

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')