Probability · Maths EE idea · Solid
Why Benford's law works
A research question to start from
Why do leading digits of many datasets follow Benford's law, and which kinds of data should not?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A question about why, answered with scale invariance and logarithms, then tested.
Mathematics you would need
- Logarithms
- Scale invariance
- Probability distributions
- Chi-squared goodness of fit
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Derive the Benford distribution from scale invariance.
- Explain why powers such as 2ⁿ follow it (equidistribution of n·log₁₀2), proving what you can.
- Test datasets you choose and explain which fail.
Scope and difficulty
Solid. Solid.
Pitfalls
- Testing data without the theory.
- Using data with a narrow range.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Benford law scale invariance derivation; powers of 2 leading digits equidistribution. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).