dgev.d: d-GEV probability density function

Description

Probability density function of duration-dependent GEV distribution

Usage

dgev.d(q, mut, sigma0, xi, theta, eta, d, eta2 = 0, tau = 0, ...)

Value

list containing vectors of density values for given quantiles. The first element of the list are the density values for the first given duration etc.

Arguments

q: vector of quantiles
mut, sigma0, xi: numeric value, giving modified location \(\tilde{\mu}\), scale offset \(\sigma_0\) and shape parameter \(\xi\).
theta: numeric value, giving duration offset \(\theta\) (defining curvature of the IDF curve)
eta: numeric value, giving duration exponent \(\eta\) (defining slope of the IDF curve)
d: positive numeric value, giving duration
eta2: numeric value, giving a second duration exponent \(\eta_{2}\) (needed for multiscaling). Default: \(\eta_2=0\).
tau: numeric value, giving intensity offset \(\tau\) (defining flattening of the IDF curve). Default: \(\tau=0\).
...: additional parameters passed to dgev

Details

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

Examples

Run this code

x <- seq(4,20,0.1)
# calculate probability density for one duration
dgev.d(q=x,mut=4,sigma0=2,xi=0,theta=0.1,eta=0.1,d=1)

# calculate probability density for different durations
ds <- 1:4
dens <- lapply(ds,dgev.d,q=x,mut=4,sigma0=2,xi=0,theta=0.1,eta=0.1)

plot(x,dens[[1]],type='l',ylim = c(0,0.21),ylab = 'Probability Density')
for(i in 2:4){
  lines(x,dens[[i]],lty=i)
}
legend('topright',title = 'Duration',legend = 1:4,lty=1:4)