BivLaplaceRL

BivLaplaceRL is an R package for bivariate and univariate Laplace transforms of residual lives, stochastic ordering concepts, and entropy measures in reliability analysis.

Residual Life Analysis

Bivariate Laplace transforms of residual lives — closed-form Gumbel results, general numerical integration, nonparametric estimation, and NBUHR/NWUHR aging class characterisation.

Reversed Residual Lives

BLt-Rrl framework: reversed hazard gradient, reversed mean residual life, and closed-form transforms for FGM and bivariate power distributions.

Univariate Methods

Univariate LT of residual life, hazard rate, mean residual life, and three stochastic orders (Lt-rl, hazard rate, MRL) with nonparametric estimation.

Stochastic Orders

Seven bivariate and three univariate stochastic order checks, each returning a logical flag and supporting diagnostic values.

Research Basis

Paper	Journal	Authors
Bivariate Laplace transform of residual lives and their properties	Communications in Statistics — Theory and Methods (2022)	Jayalekshmi S., Rajesh G., Nair N.U.
Bivariate Laplace transform order and ordering of reversed residual lives	Int. J. Reliability, Quality and Safety Engineering	Jayalekshmi S., Rajesh G.

Features

Parametric Distributions

Gumbel bivariate exponential (dgumbel_biv, sgumbel_biv, rgumbel_biv, pgumbel_biv)
Farlie-Gumbel-Morgenstern — FGM (dfgm_biv, pfgm_biv, sfgm_biv, rfgm_biv)
Bivariate power distribution (dbivpower, pbivpower, sbivpower, rbivpower)
Schur-constant distribution (sschur_biv, rschur_biv)

Bivariate Laplace Transform of Residual Lives

blt_residual() — numerical computation for any survival function
blt_residual_gumbel() — closed-form for Gumbel distribution
biv_hazard_gradient() — bivariate hazard gradient
biv_mean_residual() — bivariate mean residual life
nbuhr_test() — NBUHR/NWUHR aging class test
np_blt_residual() — nonparametric estimator
sim_blt_residual() — Monte-Carlo simulation study

Bivariate Laplace Transform of Reversed Residual Lives

blt_reversed() — for any joint CDF
blt_reversed_fgm() — closed form for FGM
blt_reversed_power() — for bivariate power distribution
biv_rhazard_gradient() — reversed hazard gradient
biv_rmrl() — reversed mean residual life

Univariate Residual Life Analysis

lt_residual() — LT of residual life: E[e^{-sX} | X > t]
hazard_rate() — hazard rate h(t) = f(t)/S(t)
mean_residual() — mean residual life m(t) = E[X-t | X>t]
np_lt_residual() — nonparametric estimator

Stochastic Orders (Bivariate)

blt_order_residual() — BLt-rl order
blt_order_reversed() — BLt-Rrl order
biv_whr_order() — weak bivariate hazard rate order
biv_wmrl_order() — weak bivariate MRL order
biv_brlmr_order() — bivariate relative MRL order
biv_wrhr_order() — weak bivariate reversed hazard rate order
biv_wrmrl_order() — weak bivariate reversed MRL order

Stochastic Orders (Univariate)

lt_rl_order() — Lt-rl order: L_X(s,t) ≤ L_Y(s,t) for all s, t
hr_order() — hazard rate order: h_X(t) ≤ h_Y(t) for all t
mrl_order() — MRL order: m_X(t) ≤ m_Y(t) for all t

Entropy Measures

shannon_entropy() — Shannon differential entropy
info_gen_function() — Golomb information generating function

Plotting

plot_blt_residual(), plot_blt_reversed()

Installation

# Install from CRAN
install.packages("BivLaplaceRL")

# Development version from GitHub
# install.packages("devtools")
devtools::install_github("itsmdivakaran/BivLaplaceRL")

Quick Start

library(BivLaplaceRL)

# 1. Simulate from Gumbel bivariate exponential
set.seed(42)
dat <- rgumbel_biv(500, k1 = 1, k2 = 1, theta = 0.5)

# 2. Nonparametric estimate of BLT of residual lives
np_blt_residual(dat, s1 = 1, s2 = 1, t1 = 0.3, t2 = 0.3)

# 3. Compare with closed-form
blt_residual_gumbel(s1 = 1, s2 = 1, t1 = 0.3, t2 = 0.3, k1 = 1, k2 = 1, theta = 0.5)

# 4. Univariate LT of residual life for Exp(1)
f  <- function(x) dexp(x, 1)
Fb <- function(x) pexp(x, 1, lower.tail = FALSE)
lt_residual(f, Fb, s = 1, t = 0.5)

# 5. Hazard rate and MRL
hazard_rate(f, Fb, t = c(0.5, 1, 2))
mean_residual(Fb, t = c(0, 0.5, 1, 2))

# 6. Check univariate stochastic orders: Exp(2) <=_hr Exp(1)?
f2  <- function(x) dexp(x, 2)
Fb2 <- function(x) pexp(x, 2, lower.tail = FALSE)
hr_order(f2, Fb2, f, Fb, t_grid = c(0.5, 1, 2))$order_holds

Authors

Mahesh Divakaran (maintainer) Research Scholar, Amity School of Applied Sciences, Amity University Lucknow imaheshdivakaran@gmail.com

S. Jayalekshmi, G. Rajesh, N. Unnikrishnan Nair Department of Statistics, Cochin University of Science and Technology

References

Jayalekshmi S., Rajesh G., Nair N.U. (2022). Bivariate Laplace transform of residual lives and their properties. Communications in Statistics — Theory and Methods. https://doi.org/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. https://doi.org/10.1142/S0218539322500061

Belzunce F., Ortega E., Ruiz J.M. (1999). The Laplace order and ordering of residual lives. Statistics & Probability Letters, 42(2), 145–156. https://doi.org/10.1016/S0167-7152(98)00202-8