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The power law is surprising. We're taught that the Gaussian distribution shows up everywhere in nature (aka the "Normal" distribution) yet here is a distributio
by abetusk 4y ago
The power law is surprising. We're taught that the Gaussian distribution shows up everywhere in nature (aka the "Normal" distribution) yet here is a distribution that converges to a power law tail.
For comparison, Zipf has a power law tail (x^{-\alpha}) whereas a Gaussian distribution falls off doubly exponentially (e^{-x^2}).
- pizza 4y agoMinor nitpick about being surprised that a power law shows up: you need to be really careful when you say something follows a power law. The appearance of a nice power law may actually be illusion, sometimes, because log-scale tends to 'squash' data with quite a lot of 'pressure'. That's because it's quite possible to have 2 lines of fit that look like they both very nicely follow a power law, but then once you go from a log-scale plot to linear plot by doing the inverse of the log, ie exponential transform, one of the 2 plots may turn out to be really crappy, actually. So, if the error bars on the log-scale plot are not in some sense really small (e.g logarithmic in themselves) already to begin with, then, you may actually be committing ~great crimes of statistics~, unknowingly.
- mdp2021 4y ago> shows up everywhere in nature Shows up "everywhere", not exclusively. For that matter, also Erlang distributions are occurring models.