A new quantity for statistical analysis: "Scaling invariable Benford distance"

TL;DR

This paper introduces the 'Scaling invariable Benford distance' and 'Benford cyclic graph' as new tools for analyzing data sets, revealing how these measures vary across distributions and with data size.

Contribution

It presents novel quantitative and graphical methods for statistical analysis based on Benford's law, applicable to any data set.

Findings

Different data sets show distinct 'Scaling invariable Benford distance' values.

The 'Benford cyclic graph' features vary across distributions.

The distance decreases with data size and stabilizes at large sizes.

Abstract

For the first time, we introduce "Scaling invariable Benford distance" and "Benford cyclic graph", which can be used to analyze any data set. Using the quantity and the graph, we analyze some date sets with common distributions, such as normal, exponent, etc., find that different data set has a much different value of "Scaling invariable Benford distance" and different figure feature of "Benford cyclic graph". We also explore the influence of data size on "Scaling invariable Benford distance", and find that it firstly reduces with data size increasing, then approximate to a fixed value when the size is large enough.