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Asymptotic Normality for Oscillation of Permutation
Published online by Cambridge University Press: 27 July 2009
Abstract
Suppose each permutation (πl,…,πn) of ( 1, …, n) has probability 1/n!. The oscillation of (πl; …, πn) is defined as Tn = | πk − πk+1|, where πn+1 = π1. It is proved that (Tn − ETn)/(var Tn)1/2 converges in distribution to N(0,1). The connection between the oscillation and the presortedness measure is also discussed.
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- Research Article
- Information
- Probability in the Engineering and Informational Sciences , Volume 7 , Issue 2 , April 1993 , pp. 227 - 235
- Copyright
- Copyright © Cambridge University Press 1993
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