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% Please edit documentation in R/BivLaplaceRL-package.R
\docType{package}
\name{BivLaplaceRL-package}
\alias{BivLaplaceRL-package}
\alias{BivLaplaceRL}
\title{BivLaplaceRL: Bivariate Laplace Transforms, Stochastic Orders, and Entropy
Measures in Reliability}
\description{
\pkg{BivLaplaceRL} provides a unified framework for three interconnected
research themes in reliability analysis and survival theory:

\strong{1. Bivariate Laplace Transform of Residual Lives}

Implements the vector Laplace transform of bivariate residual lives
\eqn{(L_{X_{t_1|t_2}}(s_1),\,L_{X_{t_2|t_1}}(s_2))}, the associated
stochastic ordering BLt-rl, and its relationships with the weak bivariate
hazard rate order, weak bivariate mean residual life order, and bivariate
relative mean residual life order.  Nonparametric estimation and NBUHR/NWUHR
aging class tests are included.
Reference: Jayalekshmi, Rajesh, and Nair (2022)
\doi{10.1080/03610926.2022.2085874}.

\strong{2. Bivariate Laplace Transform of Reversed Residual Lives}

Implements the bivariate Laplace transform of reversed (past) residual lives,
the BLt-Rrl stochastic order, and connections with weak bivariate reversed
hazard rate and reversed mean residual life orders.

\strong{3. Residual Entropy Generating Function}

Implements the dynamic information generating function (REGF), the residual
entropy of Ebrahimi and Pellerey (1995), Golomb's (1966) information
generating function, and nonparametric estimation of REGF with Monte-Carlo
simulation support.
}
\section{Parametric families}{

Gumbel bivariate exponential, Farlie-Gumbel-Morgenstern (FGM), bivariate
power, Schur-constant, and exponential distributions are built in.
}

\section{Plotting}{

\code{\link{plot_blt_residual}}, \code{\link{plot_blt_reversed}}, and
\code{\link{plot_regf}} provide ready-made visualisations.
}

\references{
Jayalekshmi S., Rajesh G., Nair N.U. (2022). Bivariate Laplace transform of
residual lives and their properties. *Communications in Statistics - Theory
and Methods*. \doi{10.1080/03610926.2022.2085874}

Jayalekshmi S., Rajesh G. Bivariate Laplace transform order and ordering of
reversed residual lives. *International Journal of Reliability, Quality and
Safety Engineering*.

Smitha S., Rajesh G., Jayalekshmi S. (2024). On residual entropy generating
function. *Journal of the Indian Statistical Association*, 62(1), 81--93.

Belzunce F., Ortega E., Ruiz J.M. (1999). The Laplace order and ordering of
residual lives. *Statistics & Probability Letters*, 42(2), 145--156.

Ebrahimi N., Pellerey F. (1995). New partial ordering of survival functions
based on the notion of uncertainty. *Journal of Applied Probability*, 32(1),
202--211.

Golomb S.W. (1966). The information generating function of a probability
distribution. *IEEE Transactions on Information Theory*, 12(1), 75--77.
}
\seealso{
Useful links:
\itemize{
  \item \url{https://itsmdivakaran.github.io/BivLaplaceRL/}
  \item \url{https://github.com/itsmdivakaran/BivLaplaceRL}
  \item Report bugs at \url{https://github.com/itsmdivakaran/BivLaplaceRL/issues}
}

}
\author{
\strong{Maintainer}: Mahesh Divakaran \email{imaheshdivakaran@gmail.com} (\href{https://orcid.org/0000-0002-3488-0857}{ORCID}) (Amity School of Applied Sciences, Amity University Lucknow)

Authors:
\itemize{
  \item S. Jayalekshmi (Department of Statistics, Cochin University of Science and Technology)
  \item G. Rajesh \email{rajeshgstat@gmail.com} (Department of Statistics, Cochin University of Science and Technology)
  \item N. Unnikrishnan Nair (Department of Statistics, Cochin University of Science and Technology)
  \item Smitha S. (K. E. College, Mannanam)
}

}
