PROBABILITY DU JOUR
You can see with the naked eye that the data in the Ariely paper was fabricated: for annual miles driven, STDEV ~ ½ mean. For a one-tailed distribution, this MUST be Uniform, flat frequ. in [a,b].
Miles per annum CANNOT be uniform SINCE they are a sum: CLT!
You can see with the naked eye that the data in the Ariely paper was fabricated: for annual miles driven, STDEV ~ ½ mean. For a one-tailed distribution, this MUST be Uniform, flat frequ. in [a,b].
Miles per annum CANNOT be uniform SINCE they are a sum: CLT!
2) Here is the story (softly) retracted from PNAS. Someone cheated in the food chain, and there was no need for the graphs below to figure it out.
economist.com/graphic-detail…
economist.com/graphic-detail…
3) The Ariely paper (cont):
This very very short video explains why ~ NO sum can be uniform.
This very very short video explains why ~ NO sum can be uniform.
Note: I used "~" because the uniform is decomposable, but into a weird combination of Bernouilli + uniform. The discrete uniform, I believe, can be indecomposable.
Note: the "MUST" is ~MUST since there are other candidate distributions (gamma, lognormal) but then must be monstrously skewed for STD to be uninformative under v. Large summation.
An interesting point concerning the scaling of noise: if the daily mean is twice the standard deviation, the annual mean must be ~ 38 times the annual standard deviation.
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