Benford’s Law, data mining, and financial fraud: a case study in New York State Medicaid data

Abstract

Benford's Law was first described by an astronomer in 1881, but physicist Frank Benford lent his name to the property in a mathematical treatise published in 1938. Behaviour of numbers described by the Law defies intuition, demonstrating that one is the most frequent (30.1%), and nine is the least frequent (4.6%). The property holds for a wide variety of numbers, including but not limited to: stock indices, river lengths, road numbers, etc. Departures from the classic Benford distribution are linked to anomalies, specifically in financial data where the property has been successfully employed in financial audits. The limitation of Benford's Law is that it identifies a relatively large pool of "candidate" anomalies that must be manually evaluated. In the present analysis of Medicaid data, multivariate cluster analysis in multiple tandem analyses is used to winnow the number of anomalies to a pool of high probability anomalies for evaluation. This approach makes the application of Benford's Law more practical.