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A talk by Chris Anderson at SciFoo (in Google) on whether the long tail a power law distribution or a lognormal distribution.
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A problem with the Long Tail
(Although an amazing number of things are powerlaws, a lot of things aren’t.
How can you tell the difference?)
(Read the text in the notes panel at the bottom for narration)
A powerlaw
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10
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0 10 20 30 40 50 60 70 80 90 100
Products
Sal
es (
$)
Shown another way
1
10
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1 10 100
Products
Sal
es (
$)
WTF?
The Missing Market
Source: Morris Rosenthal
The problem
Examples of phenomena that follow powerlaw distributions
• Species distribution among plants• Square footage of Alaskan Inuit homes• Forest fires, by size• Cities, by population• Death toll in wars• Earthquakes• Word use• Number of papers published by scientists
Examples of phenomena that follow lognormal distributions
• Concentration of elements in the earth's crust
• Latent periods of infectious diseases• Survival times after cancer diagnosis• Distribution of chemicals in the environment
(including pollution)• Species distribution among moths and
diatoms• Crystals in ice cream• Length of words in spoken conversation
What’s the difference?
Powerlaws: created by “preferential attachment” in scale-free networks.
Lognormal distributions: created by "proportionate effects" (like growing by a proportion of your weight).
Question
Assuming it all comes down to network effects, how can you predict whether the “natural shape” (free of bottlenecks and other scarcity distortions) is a powerlaw or a lognormal distribution?
