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.
Prof. Clark Kimberling, Department of Mathematics, University of Evansville
DiBenedetto, Alexander M.
"Non-parametric Statistics for Quantifying Differences in Discrete Spectra,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 11.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss1/11