dgev.d.Rd 1.77 KB
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% Generated by roxygen2: do not edit by hand
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% Please edit documentation in R/d-gev.R
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\name{dgev.d}
\alias{dgev.d}
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\title{Density function of duration dependent GEV distribution}
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\usage{
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dgev.d(q, mut, sigma0, xi, theta, eta, d, ...)
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}
\arguments{
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\item{q}{vector of quantiles}
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\item{mut, sigma0, xi}{numeric value, giving modified location, modified scale and shape parameter}
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\item{theta}{numeric value, giving duration offset (defining curvature of the IDF curve)}
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\item{eta}{numeric value, giving duration exponent (defining slope of the IDF curve)}
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\item{d}{positive numeric value, giving duration}
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\item{...}{additional parameters passed to \code{\link[evd]{dgev}}}
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}
\value{
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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
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}
\description{
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Density function of duration dependent GEV distribution
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}
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\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)
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# 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)
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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
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}
\seealso{
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\code{\link{pgev.d}}, \code{\link{qgev.d}}, \code{\link{rgev.d}}
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}