5 ms·
Do you know the temperature probability distribution in Antartica? Not all distributions are normal and not all even have a standard deviation.
by WinterMount223 5y ago
Do you know the temperature probability distribution in Antartica? Not all distributions are normal and not all even have a standard deviation.
- ianai 5y agoStandard deviation is defined by the distribution under question.
- deleted 5y ago[deleted]
- FabHK 5y agoThe 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/Chebyshev's_inequality https://en.wikipedia.org/wiki/Cauchy_distribution https://en.wikipedia.org/wiki/Cauchy_distribution
- WinterMount223 5y agoIf 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.
- ianai 5y agoYou’re the only one introducing the normal distribution here.
- nobodyandproud 5y agoWhen discussing standard deviations, what meaning is there for non-normal distribution? https://stats.stackexchange.com/questions/108578/what-does-standard-deviation-tell-us-in-non-normal-distribution#197545 https://stats.stackexchange.com/questions/108578/what-does-s...
- lanstin 5y agoFive standard deviations is not four percent, it is in the 1 in 3 Million range.
- FabHK 5y agoYes, 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).
- zmgsabst 5y ago4% 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.
- cma 5y agoThat's a bound not an expectation.
- tomrod 5y agoAn observation bound below by 5 standard deviations is at best a one in a million on a standard normal distribution.
- FabHK 5y agoYes, 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).
- FabHK 5y agoNot squared exponential (that's just an exponential), but exponential of a square, even. Anyway.