Abstract
In previous chapters the accuracy of approximations was measured using differences between two distributions, typically resulting in a measure, like the L 1 or L ∞ norm, sensitive to the variations between distributions in their bulk. In contrast, in Chap. 11, moderate deviations of distributions are developed, based on the ratio of the distribution function of the variable W of interest to that of the normal, allowing information on small probabilities in the tail to become available. Applications of the results of this chapter include the combinatorial central limit theorem, the anti-voter model, the binary expansion of a random integer, and the Curie–Weiss model.
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© 2011 Springer-Verlag Berlin Heidelberg
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Chen, L.H.Y., Goldstein, L., Shao, QM. (2011). Moderate Deviations. In: Normal Approximation by Stein’s Method. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15007-4_11
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DOI: https://doi.org/10.1007/978-3-642-15007-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15006-7
Online ISBN: 978-3-642-15007-4
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