Digital analysis: Theory and applications in auditing

Lolbert, Tamás (2006) Digital analysis: Theory and applications in auditing. Hungarian Statistical Review, 84 (SN10). pp. 148-170. ISSN 0039-0690

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Abstract

Newcomb in 1881 and Benford in 1938 independently introduced a phenomenon, that in randomly collected numbers certain digits are more often leading digits than others. They stated that the frequency of starting digits follows the logarithmic distribution, so that for any starting digit d=1 … 9, Prob(first significant dig-it=d)=log10(1+1/d). This empirical law was recognized by many mathematicians so that several possible explanations have been derived. Meanwhile the phenomenon has not only theoretical aspects, since it can be applied in detecting fraud, (deliberate) misstatements or fabrication of data, or in several other fields, but still most notably in auditing of financial statements. It has other applications as well, ranging even to the design of future computer processors. This study gives an overview on Benford’s law and its history, lists the main mathematical results and last but not least introduces the most important application, digital analysis.

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