## Journal of Applied Probability

- J. Appl. Probab.
- Volume 53, Number 4 (2016), 1265-1270.

### Improved Chen‒Stein bounds on the probability of a union

#### Abstract

We improve the Chen‒Stein bounds when applied to the probability of a union. When the probability is small, the improvement in the distance from the lower to the upper bound is roughly a factor of 2. Further improvements are determined when the events of the union are either negatively or positively dependent.

#### Article information

**Source**

J. Appl. Probab., Volume 53, Number 4 (2016), 1265-1270.

**Dates**

First available in Project Euclid: 7 December 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1481132851

**Mathematical Reviews number (MathSciNet)**

MR3581256

**Zentralblatt MATH identifier**

1358.60040

**Subjects**

Primary: 60E15: Inequalities; stochastic orderings

Secondary: 60E99: None of the above, but in this section

**Keywords**

Chen‒Stein Poisson approximation improved bounds on unions negative and positive dependencies

#### Citation

Ross, Sheldon M. Improved Chen‒Stein bounds on the probability of a union. J. Appl. Probab. 53 (2016), no. 4, 1265--1270. https://projecteuclid.org/euclid.jap/1481132851