pgev.d {IDF}

d-GEV cumulative distribution function

Description

Cumulative probability distribution function of duration-dependent GEV distribution

Usage

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

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.

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.

See Also

dgev.d, qgev.d, rgev.d

Examples

x <- seq(4,20,0.1)
prob <- pgev.d(q=x,mut=4,sigma0=2,xi=0,theta=0.1,eta=0.1,d=1)