Empirical statistical laws

An empirical statistical law or (in popular terminology) a law of statistics represents a type of behaviour that has been found across a number of datasets and, indeed, across a range of types of data sets.^[1] Many of these observances have been formulated and proved as statistical or probabilistic theorems and the term "law" has been carried over to these theorems. There are other statistical and probabilistic theorems that also have "law" as a part of their names that have not obviously derived from empirical observations. However, both types of "law" may be considered instances of a scientific law in the field of statistics.

For example, both Zipf's law and Heaps' law have been described as "empirical statistical laws"^[2] in the field of linguistics.

Examples of empirically inspired statistical laws that have a firm theoretical basis include:

• Statistical regularity
• Law of large numbers
• Law of truly large numbers
• Central limit theorem
• Regression towards the mean

Examples of "laws" with a weaker foundation include:

• Safety in numbers
• Benford's law

Examples of "laws" which are more general observations than having a theoretical background:

• Rank-size distribution

Examples of supposed "laws" which are incorrect include:

• Law of averages

See also

• laws of chance
• Hellin's law

Notes

1. Kitcher & Salmon (2009) p.51
2. Gelbukh & Sidorov (2008)

References

• Kitcher, P., Salmon, W.C. (Editors) (2009) Scientific Explanation. University of Minnesota Press. ISBN 978-0-8166-5765-0
• Gelbukh, A., Sidorov,G. (2008). Zipf and Heaps Laws’ Coefficients Depend on Language. In:Computational Linguistics and Intelligent Text Processing (pp. 332–335), Springer. ISBN 978-3-540-41687-6 . link to abstract