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I've spent a lot of time recently investigating on Benford's law. Many sources state that Benford's law can be useful when auditing accounting data. Non-fraudulent accounting data (under "good" terms) should follow Benford's law. Now my big question is: Why is it so??? What I'm looking for is a mathematical model in business/accounting that explains the phenomenon (unlike the usual roughly/heuristic approaches). No matter what, I really did not find one (searching the internet). This resource https://en.wikipedia.org/wiki/Benford%27s_law for example states some reasons for Benford's law to appear:

  • Outcomes of exponential growth processes
  • Multiplicative fluctuations
  • Scale invariance
  • Multiple probability distributions

I suppose that "Multiplicative fluctuations" could be the reason why accounting data conforms to Benford's law. But I'm not happy with this vague answer. I am missing a mathematical model explaining that behaviour. "Mathematical model" means: random variables, assumptions about them, their interaction.

Is it clear now?

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I can give you a very simple, intuitive explanation. If numbers did not follow Benford's law, it would imply that the magnitude of some random number was to some degree determined by the base in which you chose to write it.

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