Advances in Applied Probability

On dynamic mutual information for bivariate lifetimes

Jafar Ahmadi, Antonio Di Crescenzo, and Maria Longobardi

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Abstract

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.

Article information

Source
Adv. in Appl. Probab., Volume 47, Number 4 (2015), 1157-1174.

Dates
First available in Project Euclid: 11 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.aap/1449859804

Digital Object Identifier
doi:10.1239/aap/1449859804

Mathematical Reviews number (MathSciNet)
MR3433300

Zentralblatt MATH identifier
1355.94022

Subjects
Primary: 94A17: Measures of information, entropy
Secondary: 62N05: Reliability and life testing [See also 90B25] 60E99: None of the above, but in this section

Keywords
Entropy mutual information time-transformed exponential model bivariate lifetimes order statistics copula

Citation

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


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