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Estimating the Error of a Permutational Central Limit Theorem

Published online by Cambridge University Press:  27 July 2009

Chern-Ching Chao ,
Lincheng Zhao  and
Wen-Qi Liang
Chern-Ching Chao
Affiliation:
Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, R.O.C.
Lincheng Zhao
Affiliation:
Department of Mathematics, University of Science & Technology Hefei, Anhui 230026, China
Wen-Qi Liang
Affiliation:
Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, R.O.C.
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Extract

Motivated by two measures of presortedness, number of runs and oscillation of a permutation, related to the sorting problem, we derive an error bound for normal approximation to the distribution of Here, αij's are given real numbers and π is a uniformly distributed random permutation of {l,…, n}. The derivation is based on Stein's method.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 4 , October 1996 , pp. 533 - 541
Copyright
Copyright © Cambridge University Press 1996

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