On the Study of Conditional Failure Extropy

In recent years, the complementary dual of entropy, known as extropy, has emerged as a valuable tool for quantifying uncertainty in probability distributions. This work investigates the behavior of failure extropy in the multidimensional setting under dependence structures, with the objective of establishing theoretical bounds. We also introduce a novel vector-valued bivariate dynamic failure extropy (BDFEx) whose components, termed as conditional failure extropy (CFEx), capture component-wise conditional uncertainty. For CFEx, we derive several bounds and characterizations, contributing to its theoretical foundation. A new stochastic order based on CFEx has also been introduced and studied. To support empirical analysis, we propose an estimator for CFEx and evaluate its performance via Monte Carlo simulation, demonstrating its accuracy under various scenarios.