Abstract
Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in work from decades ago. Here, I briefly survey some of this history, focusing on underlying generative models that lead to these distributions. One finding is that lognormal and power law distributions connect quite naturally, and hence, it is not surprising that lognormal distributions have arisen as a possible alternative to power law distributions across many fields.
Keywords
Log-normal distributionGenerative grammarMathematicsPower lawStatistical physicsEconometricsDistribution (mathematics)Pareto distributionPower (physics)LawStatisticsComputer scienceArtificial intelligencePolitical scienceMathematical analysis
Affiliated Institutions
Related Publications
Power-law distributions in empirical data
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately,...
Power laws, Pareto distributions and Zipf's law
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously...
Spatial modelling of biodiversity at the community level
Summary Statistical modelling is often used to relate sparse biological survey data to remotely derived environmental predictors, thereby providing a basis for predictively mapp...
New Income Inequality Measures as Efficient Tools for Causal Analysis and Planning
A new system of inequality indicators is introduced in the paper. It has been elaborated for measuring income inequalities, but can serve as inequality measures for other phenom...
A State-of-the-Art Survey on Deep Learning Theory and Architectures
In recent years, deep learning has garnered tremendous success in a variety of application domains. This new field of machine learning has been growing rapidly and has been appl...
Publication Info
- Year
- 2004
- Type
- article
- Volume
- 1
- Issue
- 2
- Pages
- 226-251
- Citations
- 1793
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
1793
OpenAlex
Cite This
Michael Mitzenmacher
(2004).
A Brief History of Generative Models for Power Law and Lognormal Distributions.
Internet Mathematics
, 1
(2)
, 226-251.
https://doi.org/10.1080/15427951.2004.10129088
Identifiers
- DOI
- 10.1080/15427951.2004.10129088