On the Study of Conditional Failure Extropy

TL;DR

This paper explores the properties of failure extropy in multidimensional probability distributions, introduces a new vector-valued measure called BDFEx, and provides theoretical bounds, stochastic orders, and empirical estimators for conditional failure extropy.

Contribution

It introduces a novel vector-valued bivariate failure extropy (BDFEx) and establishes its theoretical properties, bounds, and stochastic order, along with an estimator and simulation validation.

Findings

Derived bounds and characterizations for CFEx.

Introduced a new stochastic order based on CFEx.

Validated the estimator's accuracy through Monte Carlo simulations.

Abstract

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.