Intuitive considerations clarifying the origin and applicability of the Benford law

• The Benford law appears in physical, biological and sociological sets of data.
• Benford law arises from the positional (place-value) notation.
• An alternative to Benford formulae predicting the distribution of digits in statistical data is derived.
• Application of these formulae to the analysis of infrared spectra of polymers is presented.

The diverse applications of the Benford law attract investigators working in various fields of physics, biology and sociology. At the same time, the groundings of the Benford law remain obscure. Our paper demonstrates that the Benford law arises from the positional (place-value) notation accepted for representing various sets of data. An alternative to Benford formulae to predict the distribution of digits in statistical data is derived. Application of these formulae to the statistical analysis of infrared spectra of polymers is presented. Violations of the Benford Law are discussed.

The frequencies of leading digits appearing in the data set of absorbance spectra of polymers vs. the Benford law and the proposed formulae.Figure optionsDownload as PowerPoint slide