Calculating Method of Moments Uniform Bin Width Histograms

TL;DR

This paper revisits the Method of Moments for histograms, emphasizing shape level sets and uniform bin widths, challenging traditional practices and providing new insights into histogram calculation and ranking.

Contribution

It introduces a comprehensive approach to MOM histograms with uniform bin widths, focusing on shape level sets and skewness ranking, which challenges conventional methods.

Findings

Shape level sets are central to MOM histogram calculations.

Ranking histograms by skewness improves data representation.

Calculations based on shape level sets offer new insights.

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.