Moderate deviations in Poisson approximation: a first attempt
  Poisson approximation using Stein's method has been extensively studied in the literature. The main focus has been on bounding the total variation distance. This paper is a first attempt on moderate deviations in Poisson approximation for right-tail probabilities of sums of dependent indicators. We obtain results under certain general conditions for local dependence as well as for size-bias coupling. These results are then applied to independent indicators, 2-runs, and the matching problem. 
Louis H. Y. Chen, Xiao Fang, Qi-Man Shao
math.PR