Abstract
Momentarily departing from the normal case, approximations by continuous distributions for which the methods of the previous chapters may be extended are considered in Chap. 13. The bounds developed are applied to the approximation of the distribution of the total spin of the Curie–Weiss model from statistical physics, at the critical inverse temperature, by a distribution with density proportional to exp (−x 4/12). Bounds for approximation by the exponential distribution are also derived, and applied to the spectrum of the Bernoulli Laplace Markov chain, and first passage times for Markov chains.
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© 2011 Springer-Verlag Berlin Heidelberg
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Chen, L.H.Y., Goldstein, L., Shao, QM. (2011). Non-normal Approximation. In: Normal Approximation by Stein’s Method. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15007-4_13
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DOI: https://doi.org/10.1007/978-3-642-15007-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15006-7
Online ISBN: 978-3-642-15007-4
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