## The Annals of Probability

- Ann. Probab.
- Volume 8, Number 3 (1980), 576-583.

### A Note on Domains of Partial Attraction

#### Abstract

We attempt to relate the domains of partial attraction for sums of i.i.d. random variables to some properties of a generalised regular variation. We give a new characterisation of the domain of partial attraction of the normal distribution and new sufficient conditions for a distribution to belong to a domain of partial attraction.

#### Article information

**Source**

Ann. Probab., Volume 8, Number 3 (1980), 576-583.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176994727

**Digital Object Identifier**

doi:10.1214/aop/1176994727

**Mathematical Reviews number (MathSciNet)**

MR573293

**Zentralblatt MATH identifier**

0447.60019

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 60G50: Sums of independent random variables; random walks

**Keywords**

Domains of attraction partial attraction regular variation Polya peaks infinitely divisible distributions sums of random variables

#### Citation

Maller, R. A. A Note on Domains of Partial Attraction. Ann. Probab. 8 (1980), no. 3, 576--583. doi:10.1214/aop/1176994727. https://projecteuclid.org/euclid.aop/1176994727