Mathematics – Statistics Theory
Scientific paper
2006-12-21
Mathematics
Statistics Theory
Scientific paper
This article on Benford's Law specifically and Leading Digits (Significant Digits) in general is an attempt at a bit more comprehensive account of the phenomena, seeking to re-examine the various points of views and the explanation of the phenomena. In addition, many of its aspects, implications and appropriate usages will be presented. Forensic data analysis, testing for possible fraud in tax reports for example, could be greatly aided by the new procedure suggested in this article, showing a hidden "signature within a signature" of data. This signature is determined via the unique manifestation of leading digits distribution of any given piece of honest data, be it logarithmic or otherwise. Consistent patterns are seen in such a quest for a code within that digital code. This can serve as a new robust forensic test tool to investigate fake data provided by the sophisticated and well-educated cheater already aware of Benford's Law and all its higher orders features as well, yet unable to truly concoct or mimic real life data with all its intricate and hidden inner properties. Moreover, this unique digital pattern is thought to be by far much more prevalent and general than Benford's Law itself! Such wider application of digital analysis can also significantly aide tax authorities and auditing firms in discovering accounting fraud when analyzing data that by itself does not obey Benford's Law, hence enabling accounting data that was hitherto outside the scope of the statistician to be forensically examined as well. Also of note is the finding that leading digits of chains of distributions that are linked via parameter selection are logarithmic either (1) in the limit where the number of the sequences in the chain approaches infinity, or (2) where the distribution generating a parameter is itself logarithmic.
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