% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/bivariate_laplace_reversed.R
\name{blt_reversed}
\alias{blt_reversed}
\title{Bivariate Laplace Transform of Reversed Residual Lives}
\usage{
blt_reversed(s1, s2, t1, t2, cdf_fn = NULL, theta = 0, g_form = FALSE)
}
\arguments{
\item{s1, s2}{Positive Laplace parameters.}

\item{t1, t2}{Positive truncation times (\eqn{t_i > 0}).}

\item{cdf_fn}{A function \code{function(x1, x2)} returning the joint CDF
\eqn{F(x_1,x_2)}.  Defaults to the FGM distribution.}

\item{theta}{FGM association parameter (used when \code{cdf_fn = NULL}).}

\item{g_form}{Logical; if \code{TRUE} returns the \eqn{G} form instead of
\eqn{L}.}
}
\value{
A named numeric vector \code{(L1, L2)} or \code{(G1, G2)}.
}
\description{
Computes the bivariate Laplace transform of reversed (past) residual lives.
For a random pair \eqn{(X_1,X_2)} with joint distribution function
\eqn{F(x_1,x_2)}, the transform is
\deqn{L_{t_1|t_2}(s_1) = e^{-s_1 t_1} +
  \frac{s_1 \int_0^{t_1} e^{-s_1 x_1} F(x_1, t_2)\,dx_1}{F(t_1, t_2)}}
and the associated \eqn{G} function (useful for ordering) is
\deqn{G_1(t_1,t_2) =
  \frac{\int_0^{t_1} e^{-s_1 x_1} F(x_1, t_2)\,dx_1}{
    e^{-s_1 t_1} F(t_1,t_2)}.}
}
\examples{
# FGM distribution (default)
blt_reversed(s1 = 1, s2 = 1, t1 = 0.6, t2 = 0.6)

# G form
blt_reversed(s1 = 1, s2 = 1, t1 = 0.6, t2 = 0.6, g_form = TRUE)

# User-supplied CDF
cdf <- function(x1, x2) pfgm_biv(x1, x2, theta = 0.5)
blt_reversed(s1 = 1, s2 = 1, t1 = 0.5, t2 = 0.5, cdf_fn = cdf)

}
\references{
Jayalekshmi S., Rajesh G. Bivariate Laplace transform order and ordering of
reversed residual lives. *International Journal of Reliability, Quality and
Safety Engineering*.
}
\seealso{
\code{\link{blt_reversed_fgm}}, \code{\link{blt_order_reversed}}
}
