Open Access
October, 1989 On Normal Approximations of Distributions in Terms of Dependency Graphs
Pierre Baldi, Yosef Rinott
Ann. Probab. 17(4): 1646-1650 (October, 1989). DOI: 10.1214/aop/1176991178


Bounds on the error in the normal approximation of sums of dependent random variables introduced by Stein are interpreted in terms of dependency graphs. This leads to improvements on a central limit theorem of Petrovskaya and Leontovich and recent applications by Baldi and Rinott. In particular, bounds on rates of convergence are obtained. As an application we study the normal approximation to the number of local maxima of a random function on a graph.


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Pierre Baldi. Yosef Rinott. "On Normal Approximations of Distributions in Terms of Dependency Graphs." Ann. Probab. 17 (4) 1646 - 1650, October, 1989.


Published: October, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0691.60020
MathSciNet: MR1048950
Digital Object Identifier: 10.1214/aop/1176991178

Primary: 60F05
Secondary: 05C99

Keywords: central limit theorem , dependent variables , random local maxima , rates of convergence

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 4 • October, 1989
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