Improvement of the constant in the non-uniform version of the berry-esseen theorem

Abstract

We improve the constant in non-uniform version of the Berry-Esseen theorem by using two methods, namely, Stein’s method using the concentration inequality and the method obtained from the Paditz-Siganov theorem, on which the random variables are not necessarily identically distributed and the existence of the absolute third moment is not required. By these two methods, the former yields a better constant recorded, while the latter gives an even letter constant.