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\name{reparametrizations}
\alias{reparametrizations}
\alias{phieta}
\alias{etaphi}
\title{Changes Between Parametrizations}
\description{
Given a vector \eqn{(\phi_1, \ldots, \phi_m)} representing the values of a piecewise linear concave function at
\eqn{x_1, \ldots, x_m,} \code{\link{etaphi}} returns a column vector with the entries
\deqn{{\bold{\eta}} = \Bigl(\phi_1, \Bigl(\eta_1 + \sum_{j=2}^m (x_i-x_{i-1})\eta_i\Bigr)_{i=2}^m\Bigr).}{\eta = (\phi_1, (\eta_1 + \sum_{j=2}^m (x_i-x_{i-1})\eta_i)_{i=2}^m).}
The function \code{\link{phieta}} returns a vector with the entries
\deqn{{\bold{\phi}} = \Bigl(\eta_1, \Bigl(\frac{\phi_i-\phi_{i-1}}{x_i-x_{i-1}}\Bigr)_{i=2}^m\Bigr).}{\phi = (\eta_1, ((\phi_i-\phi_{i-1})/(x_i-x_{i-1}))_{i=2}^m).}
}
\usage{etaphi(x, eta)
phieta(x, phi)}
\arguments{
\item{x}{Vector of independent and identically distributed numbers, with strictly increasing entries.}
\item{eta}{Vector with entries \eqn{\eta_i = \eta(x_i).}}
\item{phi}{Vector with entries \eqn{\phi_i = \phi(x_i).}}
}
\note{These functions are not intended to be invoked by the end user.}
\author{
Kaspar Rufibach, \email{kaspar.rufibach@gmail.com}, \cr \url{http://www.kasparrufibach.ch}
Lutz Duembgen, \email{duembgen@stat.unibe.ch}, \cr \url{https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html}}
\keyword{htest}
\keyword{nonparametric}
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