% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/chapter16_universal_life.R
\name{pxtau_ul}
\alias{pxtau_ul}
\alias{tpxtau_ul}
\title{Universal life persistency probabilities}
\usage{
pxtau_ul(qd, qw, year_end_withdrawal = TRUE)

tpxtau_ul(qd, qw, year_end_withdrawal = TRUE)
}
\arguments{
\item{qd}{Mortality probabilities.}

\item{qw}{Withdrawal probabilities.}

\item{year_end_withdrawal}{Logical scalar. If \code{TRUE}, withdrawal is
modeled at year-end and persistency is
\eqn{(1-q^{(d)})(1-q^{(w)})}. Otherwise persistency is
\eqn{1-q^{(d)}-q^{(w)}}.}
}
\value{
A numeric vector.
}
\description{
\code{pxtau_ul()} computes one-year persistency probabilities under
mortality and withdrawal.
}
\details{
\code{tpxtau_ul()} computes cumulative persistency through the end of each
policy year.
}
\examples{
qd <- c(0.001, 0.002, 0.003)
qw <- c(0.02, 0.02, 0.03)

pxtau_ul(qd, qw)
tpxtau_ul(qd, qw)

}
