Binomial approximation for sum of indicators with dependent neighborhoods

The purpose of this article is to develop a new method for binomial approximation. Following the main idea of Stein's basic framework, we managed to provide a new method for binomial approximation which allows us to get an upper bound on the total variation distance between a sum of indicator random variables with dependency neighborhoods and a properly chosen binomial distribution. A simple application of this method is also given, which enables us to obtain a total variation distance between the distribution of the number of k-length head run and a properly chosen binomial distribution.