Non-parametric Statistics for Quantifying Differences in Discrete Spectra
Alexander M. DiBenedetto · Rose-Hulman Scholar (Rose–Hulman Institute of Technology) · 2014
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.