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A comment on Eastern Antarctica sees record temperatures 70 degrees above normal. Parent comment

Re:Eastern Antarctica sees record temperatures 70 degrees ab... by FabHK on Saturday March 19, 2022 @10:46AM (#30734151)
The probability that an observation is beyond 5 standard deviations is < 1/25 = 4%, according to Chebyshev's inequality, provided the variance of the distribution is finite (which, as you say, is not guaranteed, eg. for Cauchy distributed random variables).

https://en.wikipedia.org/wiki/Chebyshev's_inequality

https://en.wikipedia.org/wiki/Cauchy_distribution

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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by tomrod on Saturday March 19, 2022 @12:32PM (#30735133)
An observation bound below by 5 standard deviations is at best a one in a million on a standard normal distribution.
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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by FabHK on Sunday March 20, 2022 @07:31AM (#30741784)
Yes, for a normal, which is known to have extremely thin tails (decaying with a squared exponential!). Chebyshev's bound holds for any possible distribution (with finite variance).
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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by FabHK on Sunday March 20, 2022 @09:52AM (#30742586)
Not squared exponential (that's just an exponential), but exponential of a square, even. Anyway.
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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by WinterMount223 on Saturday March 19, 2022 @10:56AM (#30734256)
If the observed variable is “the mean temperature in a given day”, 4% can be expected to occur relatively frequently.

Anyway until we know the probability distribution, and my intuition says that it’s definitely not Normal for wide periods of time, we can’t say if it’s significant or not.

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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by lanstin on Saturday March 19, 2022 @02:52PM (#30736565)
Five standard deviations is not four percent, it is in the 1 in 3 Million range.
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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by FabHK on Sunday March 20, 2022 @07:32AM (#30741786)
Yes, for a normal, which is known to have extremely thin tails (decaying with a squared exponential!). Chebyshev's bound holds for any possible distribution (with finite variance).
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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by ianai on Saturday March 19, 2022 @11:09AM (#30734373)
You’re the only one introducing the normal distribution here.
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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by nobodyandproud on Saturday March 19, 2022 @01:30PM (#30735696)
When discussing standard deviations, what meaning is there for non-normal distribution?

https://stats.stackexchange.com/questions/108578/what-does-s...

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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by zmgsabst on Saturday March 19, 2022 @11:06AM (#30734347)
4% would imply that we should expect about two weeks of such weather every year, in total.

Which would make this article somewhat clickbait — nothing more than “wowza, July 15th is another hot one in California!”

Since it’s currently summer, in the Southern Hemisphere.

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Re:Eastern Antarctica sees record temperatures 70 degrees ab... by cma on Saturday March 19, 2022 @12:26PM (#30735069)
That's a bound not an expectation.
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