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> all natural distributions follow that curve No, they don't. Many approximate that curve. Others do not. For examples: "Bimodal distribution of flowering tim

by dalke 10y ago

> all natural distributions follow that curve No, they don't. Many approximate that curve. Others do not. For examples: "Bimodal distribution of flowering time in a natural hybrid population of daylily (Hemerocallis fulva) and nightlily (Hemerocallis citrina)" - http://link.springer.com/article/10.1007%2Fs10265-005-0241-3 http://link.springer.com/article/10.1007%2Fs10265-005-0241-3 . http://psychology.wikia.com/wiki/Bimodal_distribution http://psychology.wikia.com/wiki/Bimodal_distribution lists other bimodal distributions: "the time between eruptions of certain geysers, the color of galaxies, the size of worker weaver ants, the age of incidence of Hodgkin's lymphoma, the speed of inactivation of the drug isoniazid in US adults, the absolute magnitude of novae, and the circadian activity patterns of those crepuscular animals that are active both in morning and evening twilight" A large number of natural distributions follow a power-law distribution. https://en.wikipedia.org/wiki/Power_law#Examples https://en.wikipedia.org/wiki/Power_law#Examples gives many examples. That said, you do not need that broad claim to make your argument.

arpa 10y ago
I humbly sit corrected. Thanks for the links!
mattkrause 10y ago
>A large number of natural distributions follow a power-law distribution. This is surprisingly debatable. People like to find power-law/scale-free distributions because it implies a neat generative story, but a lot of the "evidence" for power-law distributions is pretty weak. For example, you cannot just show that a log-log plot is linear--lots of other distributions can produce similar plots. Clauset, Shalizi, and Newman have a very readable paper where they describe 1) how to properly test for a power-law distribution, and 2) use those tests to assess the validity of some claims from the literature (spoiler: not many have "good" statistical support). Here is the paper: http://arxiv.org/abs/0706.1062 http://arxiv.org/abs/0706.1062 Shalizi has a short blog post describing the main results: http://bactra.org/weblog/491.html http://bactra.org/weblog/491.html
- dalke 10y ago
  Agreed. The old saying is "anything looks linear when plotted on a log-log graph." However, the OP was giving a rough approximation in the first place, in saying that all natural distributions follow a Gaussian curve. But Gaussian curves go from -∞ to +∞. Many of the real-world distributions must only have positive values, like heights and weights. Although for real-world purposes, they can usually be approximated as Gaussian. With that roughness in mind, I think it's okay to say that the Stefan–Boltzmann law, the inverse-square laws of Newtonian gravity and electrostatics, or Kleiber's law, which are all listed in the Wikipedia link are close to a power law to be acceptable counter-examples. (Stefan–Boltzmann assumes a perfect black body, the inverse-square laws ignore relativity, and Kleiber's law is a rule-of-thumb in the first place.)
  - mattkrause 10y ago
    Oh sure. When there's a plausible reason for thinking something is scale-free, I'm all for it. For a while though, it was en vogue to find power law distributions in all sorts of weird places (email response times, numbers of friends), and that's what I was attempting to object to!

by dalke 10y ago

arpa 10y ago

I humbly sit corrected. Thanks for the links!

mattkrause 10y ago

>A large number of natural distributions follow a power-law distribution. This is surprisingly debatable. People like to find power-law/scale-free distributions because it implies a neat generative story, but a lot of the "evidence" for power-law distributions is pretty weak. For example, you cannot just show that a log-log plot is linear--lots of other distributions can produce similar plots. Clauset, Shalizi, and Newman have a very readable paper where they describe 1) how to properly test for a power-law distribution, and 2) use those tests to assess the validity of some claims from the literature (spoiler: not many have "good" statistical support). Here is the paper: http://arxiv.org/abs/0706.1062 http://arxiv.org/abs/0706.1062 Shalizi has a short blog post describing the main results: http://bactra.org/weblog/491.html http://bactra.org/weblog/491.html

dalke 10y ago
Agreed. The old saying is "anything looks linear when plotted on a log-log graph." However, the OP was giving a rough approximation in the first place, in saying that all natural distributions follow a Gaussian curve. But Gaussian curves go from -∞ to +∞. Many of the real-world distributions must only have positive values, like heights and weights. Although for real-world purposes, they can usually be approximated as Gaussian. With that roughness in mind, I think it's okay to say that the Stefan–Boltzmann law, the inverse-square laws of Newtonian gravity and electrostatics, or Kleiber's law, which are all listed in the Wikipedia link are close to a power law to be acceptable counter-examples. (Stefan–Boltzmann assumes a perfect black body, the inverse-square laws ignore relativity, and Kleiber's law is a rule-of-thumb in the first place.)
- mattkrause 10y ago
  Oh sure. When there's a plausible reason for thinking something is scale-free, I'm all for it. For a while though, it was en vogue to find power law distributions in all sorts of weird places (email response times, numbers of friends), and that's what I was attempting to object to!