A brief history of generative models for power law and lognormal distributions

Michael Mitzenmacher

Internet Mathematics (2004)

TL;DR

Multiplicative processes generate log-normal distributions

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A brief history of generative models for power law and lognormal distributions

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Technical review of mechanisms generating power law and log-normal distributions, discussing when each applies. Essential for understanding that multiplicative processes typically generate log-normal distributions that approximate power laws only in upper tails.

Provides mathematical foundation for distinguishing between related heavy-tailed distributions and understanding their different implications.

Key Findings from Mitzenmacher (2004)

Multiplicative processes generate log-normal distributions
Log-normal approximates power law in upper tail
Different mechanisms produce different distributional forms
Historical development of generative models

A brief history of generative models for power law and lognormal distributions

Key Findings from Mitzenmacher (2004)

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