% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/utils.R
\name{rho_from_vopt}
\alias{rho_from_vopt}
\title{Convert optimal intrinsic time to rho}
\usage{
rho_from_vopt(v_opt = 10, alpha = 0.025)
}
\arguments{
\item{v_opt}{Numeric > 0. Intrinsic time at which the boundary is tightest.
Recommended default from CR23: 10.}

\item{alpha}{Numeric in (0,1). Significance level (one-sided).
For a two-sided boundary at level alpha, pass alpha/2 here.}
}
\value{
Numeric > 0. The rho tuning parameter.
}
\description{
Maps the user-specified intrinsic time \code{v_opt} (the point at which a
boundary is tightest) to the \code{rho} tuning parameter, via the Lambert W
formula of Howard et al. (2021), Proposition 3 (paper-exact).
}
\details{
\deqn{\rho = \frac{v_{opt}}{-W_{-1}(-\alpha^2 / e) - 1}}
The lower branch \eqn{W_{-1}} is defined for \code{x} in \verb{[-1/e, 0)} and returns
values \verb{<= -1}. For \code{alpha} in \verb{(0, 1)}, \code{-alpha^2/e} is always in
\verb{(-1/e, 0)}, so the branch is well-defined.
}
\examples{
rho_from_vopt(v_opt = 10, alpha = 0.025)

}
