# Big Data and Large Numbers. Interpreting Zipf's Law

arXiv: https://arxiv.org/abs/2305.02687 · HTML: https://mlsanity.com/paper/2305.02687/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 27 references that are in the map.
- First posted on arXiv 4 May 2023.

## Builds on (most cited first, 3 of 3)

- [Zipf's law holds for phrases, not words](https://mlsanity.com/paper/1406.5181/) (2014)
- [Zipf's law for word frequencies: word forms versus lemmas in long texts](https://mlsanity.com/paper/1407.8322/) (2014)
- [Bayesian inferences on uncertain ranks and orderings: Application to ranking players and lineups](https://mlsanity.com/paper/1907.04842/) (2019)

## Abstract (arXiv)

It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution that occur when the population is finite and the rank and counts of elements in the population are natural numbers. We are particularly concerned with the low-rank end of the graph of the law, the potential of noise in the law, and with the approximation of the number of types of objects at various ranks. Approximations instead of exact solutions are the center of attention. Consequences in the interpretation of Zipf's law are discussed.