Empirical analysis of Zipf's law, power law, and lognormal distributions in medical discharge reports

Abstract

Background: Bayesian modelling and statistical text analysis rely on informed probability priors to encourage good solutions.

Objective: This paper empirically analyses whether text in medical discharge reports follow Zipf's law, a commonly assumed statistical property of language where word frequency follows a discrete power-law distribution.

Method: We examined 20,000 medical discharge reports from the MIMIC-III dataset. Methods included splitting the discharge reports into tokens, counting token frequency, fitting power-law distributions to the data, and testing whether alternative distributions-lognormal, exponential, stretched exponential, and truncated power-law-provided superior fits to the data.

Result: Discharge reports are best fit by the truncated power-law and lognormal distributions. Discharge reports appear to be near-Zipfian by having the truncated power-law provide superior fits over a pure power-law.

Conclusion: Our findings suggest that Bayesian modelling and statistical text analysis of discharge report text would benefit from using truncated power-law and lognormal probability priors and non-parametric models that capture power-law behavior.

Keywords: Data mining; MIMIC-III dataset; Machine learning; Maximum likelihood estimation; Power-law with exponential cut-off; Statistical distributions.