% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/bivariate_laplace_residual.R
\name{np_blt_residual}
\alias{np_blt_residual}
\title{Nonparametric Estimator for the Bivariate Laplace Transform of Residual Lives}
\usage{
np_blt_residual(data, s1, s2, t1 = 0, t2 = 0)
}
\arguments{
\item{data}{A two-column numeric matrix or data frame with columns for
\eqn{X_1} and \eqn{X_2}.}

\item{s1, s2}{Positive Laplace parameters.}

\item{t1, t2}{Non-negative truncation ages.}
}
\value{
A named numeric vector \code{(L1_hat, L2_hat)}.
}
\description{
Given a bivariate sample \eqn{(X_{1i}, X_{2i}),\; i=1,\ldots,n}, estimates
\deqn{\hat{L}^*_{1}(s_1; t_1, t_2)
  = \frac{\sum_{i:X_{1i}>t_1,\,X_{2i}>t_2}
    \int_{t_1}^{X_{1i}} e^{-s_1 u}\,du}{e^{-s_1 t_1} \cdot
    \#\{X_{1i}>t_1,X_{2i}>t_2\}}}
and analogously for the second component, using the empirical survival
function as described in Jayalekshmi et al. (2022), Section 6.
}
\examples{
set.seed(123)
dat <- rgumbel_biv(200, k1 = 1, k2 = 1, theta = 0.5)
np_blt_residual(dat, s1 = 1, s2 = 1, t1 = 0.3, t2 = 0.3)

# Compare with closed form
blt_residual_gumbel(s1 = 1, s2 = 1, t1 = 0.3, t2 = 0.3, theta = 0.5)

}
\references{
Jayalekshmi S., Rajesh G., Nair N.U. (2022), Section 6.
\doi{10.1080/03610926.2022.2085874}
}
\seealso{
\code{\link{blt_residual_gumbel}}, \code{\link{sim_blt_residual}}
}
