Calculating Method of Moments Uniform Bin Width Histograms

Abstract

A clear articulation of Method of Moments (MOM) Histograms is instructive and has waited 121 years since 1895. Also of interest are enabling uniform bin width (UBW) shape level sets. Mean-variance MOM uniform bin width frequency and density histograms are not unique, however ranking them by histogram skewness compared to data skewness helps. Although theoretical issues rarely take second place to calculations, here calculations based on shape level sets are central and challenge uncritically accepted practice. Complete understanding requires familiarity with histogram shape level sets and arithmetic progressions in the data.