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tsunamifury 5 hours ago

Bell curves are everywhere because all distributions of any properties clump in some way at some level. The basics of any probability shows this. The result is you “seeing” bell curves everywhere. Aka clumps.

This is a tautology to the extreme.

abetusk 2 hours ago | parent | next [-]

No, that's not true.

If sums of independent identically distributed random variables converge to a distribution, they converge to a Levy stable distribution [0]. Tails of the Levy stable distribution are power law, which makes them not Gaussian.

[0] https://en.wikipedia.org/wiki/Stable_distribution

D-Machine 4 hours ago | parent | prev | next [-]

Yup. And in general more heavy-tailed bumps are in fact better models (assuming normality tends to lead to over-confidence). Really think the universality is strictly mathematical, and actually rare in nature.

jibal 3 hours ago | parent | prev [-]

First, every mathematical theorem is a tautology ... don't conflate "tautological" with "obvious".

Second, your "aka" is incorrect --- there is all sorts of clumping that is not a normal distribution.

thaumasiotes 3 hours ago | parent [-]

As I'm sure tsunamifury would agree, it is incredibly common for people to label "bell curves" by eyeball, regardless of whether they are normal curves. To most people, "clumping" in a one-dimensional spectrum is all they mean by the phrase "bell curve".

D-Machine 2 hours ago | parent | next [-]

This was sort of my reading as well: I took "clumping" to mean "bump-shaped".

tsunamifury 2 hours ago | parent | prev [-]

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