# pgev.d: d-GEV cumulative distribution function In IDF: Estimation and Plotting of IDF Curves

## Description

Cumulative probability distribution function of duration-dependent GEV distribution

## Usage

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

## 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 τ (defining flattening of the IDF curve). Default: τ=0. eta2 numeric value, giving a second duration exponent η_2 (needed for multiscaling). Default: NULL, treated as η_2=η. ... additional parameters passed to pgev

## 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 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

 1 2 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) 

IDF documentation built on April 9, 2021, 5:07 p.m.