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Bounded normal approximation in simulations of highly reliable Markovian systems
Abstract
In this paper, we give necessary and sufficient conditions to ensure the validity of confidence intervals, based on the central limit theorem, in simulations of highly reliable Markovian systems. We resort to simulations because of the frequently huge state space in practical systems. So far the literature has focused on the property of bounded relative error. In this paper we focus on ‘bounded normal approximation’ which asserts that the approximation of the normal law, suggested by the central limit theorem, does not deteriorate as the reliability of the system increases. Here we see that the set of systems with bounded normal approximation is (strictly) included in the set of systems with bounded relative error.
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“Note that under the conditions of Theorem 4.2, the minimax estimator enjoys the bounded normal approximation property (Tuffin, 1999).”
From The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting (2017) · cites this paper as Tuffin, 1999
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Cited by 10
Research works printed but not linked: 13
- [2] Carrasco J. A. (1992). Failure distance based on simulation of repairable fault tolerant systems. In Proc. 5th Internat. Conference on Modeling Techniques and Tools for Computer Performance Evaluation, pp. 351–365.
- 10.1109/12.40849 · doi:10.1109/12.40849
- 10.1287/mnsc.40.3.333 · doi:10.1287/mnsc.40.3.333
- 10.1016/0029-5493(84)90060-8 · DOI
- 10.2307/1428177 · doi:10.2307/1428177
- 10.1109/12.123381 · doi:10.1109/12.123381
- Bentkus, 1996, The Berry–Eséen bound for Student's statistic, Ann. Prob., 24, 491, 10.1214/aop/1042644728 · doi:10.1214/aop/1042644728
- Feller, 1966, An Introduction to Probability Theory and its Applications, II
- 10.1007/BF02187098 · doi:10.1007/bf02187098
- 10.1007/978-1-4612-4384-7 · DOI · Paper page
- 10.1287/mnsc.41.3.524 · doi:10.1287/mnsc.41.3.524
- 10.1214/aop/1176992073 · doi:10.1214/aop/1176992073
- 10.1007/978-94-009-5819-7 · DOI · Paper page
Metadata
- Authors
- Tuffin, B.
- Venue
- Journal of Applied Probability
- Publisher
- Cambridge University Press (CUP)
- Published
- 1999-12
- Volume
- 36
- Issue
- 4
- Pages
- 974-986
- ISSN
- 0021-9002
- 1475-6072
- Cited by
- 10
- Language
- en
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