# qgev.d: d-GEV quantile function In IDF: Estimation and Plotting of IDF Curves

 qgev.d R Documentation

## 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.

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 March 18, 2022, 7:44 p.m.