Validating Benfordness on contaminated data

Abstract

Benford’s law is a mathematical model, very recurrent in practice for a wide variety of datasets, used to represent the frequencies of digits. A well-established usage of Benfordness statistical testing lies within investigations aimed to ascertain if balance sheet and income statement data are genuine. A typical, frustrating problem of Benfordness statistical tests on big, practical datasets is that they often provide p-valuessmaller than expected when the Benfordness null hypothesis is very realistic. A possible reason is that data are contaminated by some kind of noise. In this paper we propose the deconvolution approach to alleviate this issue, using both simulated and real data.