Predictability of operational processes over finite horizon |
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Authors: | Nader Ebrahimi S.N.U.A. Kirmani Ehsan S. Soofi |
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Affiliation: | 1. Division of Statistics, Northern Illinois University, DeKalb, Illinois 60155;2. Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa 50614;3. Lubar School of Business, University of Wisconsin‐Milwaukee, Milwaukee, Wisconsin 53201 |
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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. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011 |
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Keywords: | Bayesian predictive distribution entropy maintenance minimal repair mixed Poisson processes nonhomogeneous Poisson processes reliability renewal processes stochastic orderings |
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