An Algorithm to Estimate a Nonuniform Convergence Bound in the Central Limit Theorem

Abstract

A nonuniform version of the Berry-Esseen bound has been proved. The most important feature of the new bound is a monotonically decreasing function C(|t|) instead of the universal constant C=29.1174: C(|t|)<C if |t| > 3.2, and C(|t|) tends to 1+e if |t| is increasing. The function C(|t|) has very complex analytical expression based on indicator functions. A general algorithm was developed in order to estimate values of C(|t|) for an arbitrary t.