Multivariate dynamic information

Ebrahimi, Nader; Kirmani, S. N. U. A.; Soofi, Ehsan S.

doi:10.1016/j.jmva.2005.08.004

Cited by 33 publications

(45 citation statements)

References 30 publications

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“…We remark that other types of dynamic information measures for bivariate distributions have been studied by Sunoj and Linu [30]. Moreover, in agreement with (2), the mutual information M X,Y (s, t) satisfies the following identity (see [14,Equation (13)]):…”

Section: Mutual Information For Residual Lifetimesmentioning

confidence: 57%

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On dynamic mutual information for bivariate lifetimes

2015

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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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Section: Mutual Information For Residual Lifetimesmentioning

confidence: 57%

“…Various other results have been pinpointed in [14], such as the following property: if X and Y are exchangeable then…”

Section: Mutual Information For Residual Lifetimesmentioning

confidence: 99%

On dynamic mutual information for bivariate lifetimes

2015

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“…Extensions to multivariate information measures are given in Ebrahimi et al [10] . Let (X 1 , X 2 ) be a vector of nonnegative random variables.…”

Section: Multivariate Information Measuresmentioning

confidence: 99%

“…If F is absolutely continuous with respect to G, the discrimination information function between two bivariate residual lifetime distributions is [10] …”

Section: Multivariate Information Measuresmentioning

confidence: 99%

Global and Dynamic Information Measures for Reliability

Ebrahimi

Soofi

2014

Wiley StatsRef: Statistics Reference Online

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In modeling a duration variable, such as the lifetime of an object as it ages, consideration of the age partitions the support of the lifetime distribution progressively and induces truncated distributions for the past and residual lifetimes. Global information measures of the distribution of the entire lifetime do not change with the age, and thus are static. Information measures of the past and residual lifetime distributions are functions of the age, and hence are dynamic. This article presents an overview of the global and dynamic Shannon entropy, Kullback–Leibler information, and mutual information. Examples include information measures for parallel and series systems, proportional hazard, exponential, and Pareto models.

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“…with equality if and only if X n and X n−1 are stochastically independent [3,16]. On rewriting (8) as…”

Section: Predictive Information Measurementioning

confidence: 99%

Predictability of operational processes over finite horizon

Ebrahimi

Kirmani

Soofi

2011

Naval Research Logistics

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Abstract:Operational processes are usually studied in terms of stochastic processes. The main information measure used for predictability of stochastic processes is the entropy rate, which is asymptotic conditional entropy, thus not suitable for application over a finite horizon. We use the conditional entropy to study the predictability of stochastic processes over the finite horizon. It is well-known that the conditional entropies of stationary processes decrease as the processes evolve, implying that, on average, their pasts become more informative about prediction of their future outcomes. Some important operational processes such as martingale, models for maintenance policies, nonhomogeneous Poisson, and mixed Poisson processes are nonstationary. We show that as a nonstationary process evolves, it may provide more information or less information about the future state of the system. We develop results for comparing the predictability of stochastic processes.

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Multivariate dynamic information

Cited by 33 publications

References 30 publications

On dynamic mutual information for bivariate lifetimes

On dynamic mutual information for bivariate lifetimes

Global and Dynamic Information Measures for Reliability

Predictability of operational processes over finite horizon

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