Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 47, Number 4 (2015), 1157-1174.
On dynamic mutual information for bivariate lifetimes
We consider dynamic versions of the mutual information of lifetime distributions, with a focus on past lifetimes, residual lifetimes, and mixed lifetimes evaluated at different instants. This allows us to study multicomponent systems, by measuring the dependence in conditional lifetimes of two components having possibly different ages. We provide some bounds, and investigate the mutual information of residual lifetimes within the time-transformed exponential model (under both the assumptions of unbounded and truncated lifetimes). Moreover, with reference to the order statistics of a random sample, we evaluate explicitly the mutual information between the minimum and the maximum, conditional on inspection at different times, and show that it is distribution-free in a special case. Finally, we develop a copula-based approach aiming to express the dynamic mutual information for past and residual bivariate lifetimes in an alternative way.
Adv. in Appl. Probab., Volume 47, Number 4 (2015), 1157-1174.
First available in Project Euclid: 11 December 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Ahmadi, Jafar; Di Crescenzo, Antonio; Longobardi, Maria. On dynamic mutual information for bivariate lifetimes. Adv. in Appl. Probab. 47 (2015), no. 4, 1157--1174. doi:10.1239/aap/1449859804. https://projecteuclid.org/euclid.aap/1449859804