## The Annals of Probability

- Ann. Probab.
- Volume 17, Number 4 (1989), 1277-1699

### On Normal Approximations of Distributions in Terms of Dependency Graphs

#### Abstract

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.

#### Article information

**Source**

Ann. Probab. Volume 17, Number 4 (1989), 1646-1650.

**Dates**

First available: 19 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aop/1176991178

**JSTOR**

links.jstor.org

**Digital Object Identifier**

doi:10.1214/aop/1176991178

**Mathematical Reviews number (MathSciNet)**

MR1048950

**Zentralblatt MATH identifier**

0691.60020

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 05C99: None of the above, but in this section

**Keywords**

Central limit theorem dependent variables rates of convergence random local maxima

#### Citation

Baldi, Pierre; Rinott, Yosef. On Normal Approximations of Distributions in Terms of Dependency Graphs. The Annals of Probability 17 (1989), no. 4, 1646--1650. doi:10.1214/aop/1176991178. http://projecteuclid.org/euclid.aop/1176991178.