Approximations of normal distribution by its q-generalizations

Abstract

A concept of q-generalization of normal distribution arises in the context of statistical mechanics. In this article, we introduce a q-generalization of normal approximation. By using Stein's method, zero and square bias approaches are applied to derive the bound in q-normal approximation. Our results also cover the bound of normal approximation for Student’s tdistribution.

Keywords

• coupling approach
• non-normal approximation
• q-gaussian distribution
• size bias distribution
• square bias distribution