This paper introduces three statistics for comparing discrete spectra. Abstractly, a discrete spectrum (histogram with n bins) can be thought of as an ordered n-tuple. These three statistics are defined as comparisons of two n-tuples, representing pair-wise, ordered comparisons of bin heights. This paper defines all three statistics and formally proves the first one is a metric, while providing compelling evidence the other two are metrics. It shows that these statistics are gamma distributed, and for n ≥ 10, approximately normally distributed. It also discusses a few other properties of all three associated metric spaces.

Author Bio

Alexander M. DiBenedetto graduated from the University of Evansville in the spring of 2014 with majors in Physics and Applied Mathematics, as well as a minor in Computer Science. His research interests are focused on the intersection of these three disciplines; especially, the P versus NP problem and using particle physics simulations as a tool for creating better experiments. He plans to gain industry programming experience for two years before moving on to a doctoral program in either Physics or Computer Science, with the ultimate goal of professorship.