BivLaplaceRL

Bivariate Laplace Transforms, Stochastic Orders, and Entropy Measures in Reliability

Implements methods for bivariate Laplace transforms of residual lives and reversed residual lives, associated stochastic ordering concepts, and dynamic entropy measures for reliability analysis. The package covers three primary research areas: (1) Bivariate Laplace transform of residual lives and stochastic comparisons based on the bivariate Laplace transform order of residual lives (BLt-rl), including weak bivariate hazard rate, mean residual life, and relative mean residual life orders, nonparametric estimation, and NBUHR/NWUHR aging class characterisation (Jayalekshmi, Rajesh, and Nair, 2022, <doi:10.1080/03610926.2022.2085874>); (2) Bivariate Laplace transform order of reversed residual lives (BLt-Rrl), reversed hazard gradient, reversed mean residual life, and the associated stochastic orders (weak bivariate reversed hazard rate, weak bivariate reversed mean residual life); (3) Residual entropy generating function, a dynamic version of Golomb's (1966) information generating function whose derivative yields the residual entropy of Ebrahimi and Pellerey (1995), with nonparametric estimation and distribution characterisation. Parametric families supported include the Gumbel bivariate exponential, Farlie-Gumbel-Morgenstern (FGM), bivariate power, and Schur-constant distributions. Plotting utilities and a simulation framework for evaluating estimator performance are also provided.

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