Benford's Law and it's application to the tax declaration

Abstract

Benford’s Law, also referred to as the first digit Law, is somewhat of a counterintuitive law of nature that applies to numbers, more specifically to their distribution. Benford was not the only one to study such law, many mathematicians have attempted to understand the way numbers are distributed. Frank Benford, a physicist working for the Genereal Electric Company, made a very important observation by looking at the logarithmic tables. Such tables, were more consumed where the numbers had one as their first digit. Rather than just focusing on data, Benford also provided some very important empirical evidence. The innovation introduced by Benford consisted in using data that was diversified as much as possible. His objective was to verify his theory in the most unbiased way possible. By taking 20229 uncorrelated data sets, Benford was able to show that the frequency of the first digit of each number did in fact follow a precise distribution. It is in this precise moment that the Benford’s law began gaining more notoriety.The scope of this thesis will firstly consist in providing a general background to the definition of Benford’s law and all the its possible applications. We will then italian’s tax declaration to show how Benford’s law can detect possible tax evasion or erroneous mistakes. The data, finally, wil be provided to us by the public office of the Veneto region.