Variations on the Newcomb-Benford Law

TL;DR

This paper explores the Newcomb-Benford Law, proposing a generalized bin distribution to better fit data with deviations from the law, enhancing forensic and scientific data analysis.

Contribution

It introduces a generalized distribution extending the Newcomb-Benford Law to accommodate deviations in natural data sets.

Findings

Proposes a new generalized bin distribution.

Demonstrates improved data fitting over the traditional law.

Provides a framework for analyzing deviations in physical constants.

Abstract

The Newcomb-Benford Law, which is also called the first digit phenomenon, has applications in diverse phenomena ranging from social and computer networks, engineering systems, natural sciences, and accounting. In forensics, it has been used to determine intrusion in a computer server based on the measured expectations of first digits of time varying values of data, and to check whether the information in a data base has been tampered with. There are slight deviations from the law in certain natural data, as in fundamental physical constants, and here we propose a more general bin distribution of which the Newcomb-Benford Law is a special case so that it can be used to provide a better fit to such data, and also open the door to a mathematical examination of the origins of such deviations.