## The Annals of Probability

### Nonuniform Central Limit Bounds with Applications to Probabilities of Deviations

R. Michel

#### Abstract

For the distribution of the standardized sum of independent and identically distributed random variables, nonuniform central limit bounds are proved under an appropriate moment condition. From these theorems a condition on the sequence $t_n, n \in \mathbb{N}$, is derived which implies that $1 - F_n(t_n)$ is equivalent to the corresponding deviation of a normally distributed random variable. Furthermore, a necessary and sufficient condition is given for $1 - F_n(t_n) = o(n^{-c/2}t_n^{2 + c})$.

#### Article information

Source
Ann. Probab. Volume 4, Number 1 (1976), 102-106.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996186

Digital Object Identifier
doi:10.1214/aop/1176996186

Mathematical Reviews number (MathSciNet)
MR391226

Zentralblatt MATH identifier
0337.60026

JSTOR