The Newcomb-Beford Law is based on the uneven distribution of digits observed in many real world datsets under certain conditions.

Applications:

• Modeling: If a certain set of values follows Benford’s Law then model’s for the corresponding predicted values should also follow Benford’s Law.

• Fraud detection: Manipulated or fraudulent data do not trend to confirm to Benford’s Law, whereas regular data do.

• Irregularities in Price Data

Requirements:

1. The numbers need to be random and not assigned, with no imposed minimums or maximums.

2. The numbers should cover several orders of magnitude, and the dataset should be large. Recommendations in the literature call for 100 to 1,000 samples as a minimum, though Benford’s law has been shown to hold true for datasets containing as few as 50 numbers.

3. For more details, check Wikipedia!

Implementation:

• Use Chi-Square Test to see, if the actual distribution differs significantly from the distribution predicted by Newcomb-Benfords law.

• Use Kolmogorov–Smirnov test or Kuiper test in case of smaller sample sizes

• Example implementation in Python