dgev.d.Rd 1.59 KB
Newer Older
 Christoph Ritschel committed Jan 22, 2018 1 % Generated by roxygen2: do not edit by hand  2 % Please edit documentation in R/d-gev.R  Rust Henning committed Feb 03, 2016 3 4 \name{dgev.d} \alias{dgev.d}  5 \title{Density function of duration dependent GEV distribution}  Rust Henning committed Feb 03, 2016 6 \usage{  7 dgev.d(q, mut, sigma0, xi, theta, eta, d, ...)  Rust Henning committed Feb 03, 2016 8 9 } \arguments{  10 \item{q}{vector of quantiles}  Rust Henning committed Feb 03, 2016 11   12 \item{mut, sigma0, xi}{numeric value, giving modified location, modified scale and shape parameter}  Rust Henning committed Feb 03, 2016 13   14 \item{theta}{numeric value, giving duration offset (defining curvature of the IDF curve)}  Rust Henning committed Feb 03, 2016 15   16 \item{eta}{numeric value, giving duration exponent (defining slope of the IDF curve)}  Rust Henning committed Feb 03, 2016 17   18 \item{d}{numeric value, giving duration}  Rust Henning committed Feb 03, 2016 19   20 \item{...}{additional parameters passed to \code{\link[evd]{dgev}}}  Rust Henning committed Feb 03, 2016 21 22 } \value{  23 24 list containing vectors of density values for given quantiles the first element of the list are the dens. values for the first given duration and so on  Rust Henning committed Feb 03, 2016 25 26 } \description{  27 Density function of duration dependent GEV distribution  Rust Henning committed Feb 03, 2016 28 }  29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 \details{ The duration dependent GEV distribution is defined after [Koutsoyannis et al., 1998]: \deqn{ G(x)= exp[-{ 1+\xi(x/\sigma(d)-\mu_t) }^(-1/\xi)] } with the duration dependent scale \eqn{\sigma(d)=\sigma_0/(d+\theta)^\eta} and modified location parameter \eqn{\mu_t=\mu/\sigma(d)}. } \examples{ x <- seq(4,20,0.1) dens <- dgev.d(q=x,mut=4,sigma0=2,xi=0,theta=0.1,eta=0.1,d=1:4) 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) } \references{ Koutsoyannis et al., 1998, doi:10.1016/S0022-1694(98)00097-3  Rust Henning committed Feb 03, 2016 48 49 } \seealso{  50 \code{\link{pgev.d}}, \code{\link{qgev.d}}, \code{\link{rgev.d}}  Rust Henning committed Feb 03, 2016 51 }