# Asymptotically normal estimators for Zipf's law

## TL;DR

This paper develops asymptotically normal estimators for the exponent in Zipf's law, enabling more accurate statistical analysis of word frequency distributions in texts.

## Contribution

It introduces new estimators based on word diversity statistics that are asymptotically normal, improving inference for Zipf's law parameters.

## Key findings

- Estimators are asymptotically normal under the infinite urn model.
- The method provides consistent estimates of the Zipf exponent.
- Application to real texts demonstrates effectiveness.

## Abstract

Zipf's law states that sequential frequencies of words in a text correspond to a power function. Its probabilistic model is an infinite urn scheme with asymptotically power distribution. The exponent of this distribution must be estimated. We use the number of different words in a text and similar statistics to construct asymptotically normal estimators of the exponent.