Non-uniform bounds on normal approximation by Stein’s Method and bounded monotone size biased couplings

Abstract

This dissertation contains two main parts. First, we give a non-uniform exponential bound on normal approximation by using the Stein’s method and bounded monotone size biased couplings. Second, applications of the main theorem to give the bound on normal approximation for sum of independent random variables, the number of bulbs on at the terminal time in the lightbulb process, and the number of m runs are provided.