Bivariate cumulative residual entropy of equilibrium distribution of order n

Nair, Sunoj, and Rajesh (2023) have introduced the cumulative residual entropy (CRE) of order n and studied its importance in reliability theory. This article addresses that extending this measure to higher dimensions and studies its properties. We use this measure to characterize some well-known bivariate lifetime models and study their relations with reliability measures, such as product moment residual life and vector-valued failure rates. Several properties are obtained, including monotonicity and bounds based on well-known Frechet-Hoeffding bounds. Moreover, we also find an implication between bivariate CRE and positively (negatively) quadrant-dependent PQD (NQD) distributions.