pgev.d.Rd 1.44 KB
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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/d-gev.R
\name{pgev.d}
\alias{pgev.d}
\title{Distribution function of duration dependent GEV distribution}
\usage{
pgev.d(q, mut, sigma0, xi, theta, eta, d, ...)
}
\arguments{
\item{q}{vector of quantiles}

\item{mut, sigma0, xi}{numeric value, giving modified location, modified scale and shape parameter}

\item{theta}{numeric value, giving duration offset (defining curvature of the IDF curve)}

\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]{pgev}}}
}
\value{
list containing vectors of probability values for given quantiles 
the first element of the list are the prob. values for the first given duration and so on
}
\description{
Distribution function of duration dependent GEV distribution
}
\details{
The duration dependent GEV distribution is defined after 
[Koutsoyannis et al., 1998]:
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\deqn{G(x)= \exp[-\left( 1+\xi(x/\sigma(d)-\mu_t) \right)^{-1/\xi}] } 
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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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prob <- pgev.d(q=x,mu=4,sigma0=2,xi=0,theta=0.1,eta=0.1,d=1)
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}
\references{
Koutsoyannis et al., 1998, doi:10.1016/S0022-1694(98)00097-3
}
\seealso{
\code{\link{dgev.d}}, \code{\link{qgev.d}}, \code{\link{rgev.d}}
}