Benford's Law, its applicability and breakdown in the IR Spectra of polymers

TL;DR

This study investigates the applicability of Benford's Law to IR spectra of polymers, finding it applies to absorbance but not transmittance spectra, likely due to their physical and logarithmic relationships.

Contribution

It demonstrates that Benford's Law applies to absorbance spectra of polymers and explains its breakdown in transmittance spectra based on physical constraints and logarithmic relations.

Findings

Benford's Law applies to absorbance spectra of polymers.

Transmittance spectra do not follow Benford's Law due to physical restrictions.

Logarithmic dependence explains the applicability of Benford's Law in spectral data.

Abstract

Infrared spectra of various polymers were treated statistically. It was established that for the absorbance spectra the Benford distribution of leading digits takes place, whereas the distribution of leading digits for transmittance spectra is random. This observation may be explained by the fact that the value of transmittance Tr is restricted, due to the physical reasons, whereas the value of absorbance is not. Moreover, the transmittance and absorbance A are interrelated by the logarithmic dependence . This observation supplies the idea that the Benford's law is valid in the situations, when logarithmic dependencies take place.