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The asymptotic joint normality of the numbers of upper records, lower records and inversions in a random sequence

Part of: Limit theorems Combinatorics

Published online by Cambridge University Press:  14 July 2016

Chern-Ching Chao ,
Yi-Liang Chen  and
Wei-Hou Cheng
Chern-Ching Chao*
Affiliation:
Academia Sinica, Taipei
Yi-Liang Chen*
Affiliation:
Aletheia University
Wei-Hou Cheng*
Affiliation:
Tamkang University
*
∗ Postal address: Institute of Statistical Science, Academia Sinica, Taipei, Taiwan 115, Republic of China.
∗∗ Postal address: Department of Mathematical Statistics and Actuarial Science, Aletheia University, Tamsui, Taiwan 251, Republic of China.
∗∗∗ Postal address: Department of Mathematics, Tamkang University, Tamsui, Taiwan 251, Republic of China. Email address: [email protected]
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Abstract

We derive the asymptotic joint normality, by a martingale approach, for the numbers of upper records, lower records and inversions in a random sequence.

Keywords

Asymptotic joint normalitymartingale central limit theorem

MSC classification

Primary: 05A16: Asymptotic enumeration 60F05: Central limit and other weak theorems
Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 257 - 263
Copyright
Copyright © Applied Probability Trust 2003 

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