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December 2015 On dynamic mutual information for bivariate lifetimes
Jafar Ahmadi, Antonio Di Crescenzo, Maria Longobardi
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Adv. in Appl. Probab. 47(4): 1157-1174 (December 2015). DOI: 10.1239/aap/1449859804

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.

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Jafar Ahmadi. Antonio Di Crescenzo. Maria Longobardi. "On dynamic mutual information for bivariate lifetimes." Adv. in Appl. Probab. 47 (4) 1157 - 1174, December 2015. https://doi.org/10.1239/aap/1449859804

Information

Published: December 2015
First available in Project Euclid: 11 December 2015

zbMATH: 1355.94022
MathSciNet: MR3433300
Digital Object Identifier: 10.1239/aap/1449859804

Subjects:
Primary: 94A17
Secondary: 60E99 , 62N05

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

Rights: Copyright © 2015 Applied Probability Trust

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Vol.47 • No. 4 • December 2015
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