Cumulative probability distribution function of duration-dependent GEV distribution
Usage
pgev.d(q, mut, sigma0, xi, theta, eta, d, tau = 0, eta2 = 0, ...)
Value
list containing vectors of probability values for given quantiles.
The first element of the list are the probability values for the first given duration etc.
Arguments
q
vector of quantiles
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)
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 pgev
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.