I just checked out the distribution of a series of throws for the sum of two dice, which has a triangular distribution. The mean is 7 and the standard deviation is 2.45. No points are more than 2.02 SDs away from the mean.

Lots of Wall Street types have gotten in trouble lately assuming Gaussian distributions of events that are nothing like Gaussian.

He did apply elementary stats, too, by simply calculating the area under a Gaussian curve for +/- 3 sigma, then raising it to the 858th power. The probability of any one of those points being less than 3 sigma is the area, or 0.997…, therefore the probability of all of those being less than 3 sigma is 0.997^858.

The 3 sigma probability, btw, holds for normal distributions and could be quite different for another distribution.

Re: Willis Eschenbach (#25), Maybe, maybe not. Without some other information, you really can’t make that assumption. The rounding mechanism could easily explain this, btw, since some otherwise 3 sigma values may have been rounded down. Dunno…

Mark

My best to all,

w.

Whoa UC. You’re out of my league already.

My only point was that the definition of standard deviation says that plus or minus 1 SD contains roughly 68% of the values, 2 SD contains 95% of the values and 3 SD contains 99% of the values.

What I understood Willis to be saying was that there are 858 data points, therefore 1% of them, or roughly 9, should be outside 3 SD of the mean, whereas he identified that no points were, thus throwing into doubt the accuracy of the calculations.

But maybe I have it wrong……….. Apologies to you in advance if I have.

Yes, serious question.

(normcdf(3,0,1)-normcdf(-3,0,1))^858

ans =

0.0983170715220416

Quite rare, ok, but after standardizing a heavily correlated series the number might be 0.2 or something like that, right ?

Is that a serious question? Consideration of elementary stats and definitions of Standard Deviation will get you there if it is.

http://oregonstate.edu/admissions/blog/2008/12/18/osu-professor-to-head-noaa/

President-elect Barack Obama has tapped Oregon State University professor Jane Lubchenco, one of the nation’s most prominent marine biologists, to head the National Oceanic and Atmospheric Administration.

Who is Jane?
http://www.sciencedaily.com/releases/2008/02/080214144547.htm

A review of all available ocean data records concludes that the low-oxygen events which have plagued the Pacific Northwest coast since 2002 are unprecedented in the five decades prior to that, and may well be linked to the stronger, persistent winds that are expected to occur with global warming.
In a new study in the journal Science, researchers from Oregon State University outline a “potential for rapid reorganization” in basic marine ecosystems and the climatic forces that drive them, and suggest that these low-oxygen, or “hypoxic” events are now more likely to be the rule rather than the exception.

“In this part of the marine environment, we may have crossed a tipping point,” said Jane Lubchenco, the Wayne and Gladys Valley Professor of Marine Biology at OSU, and the lead scientist for PISCO, the Partnership for Interdisciplinary Studies of Coastal Oceans.

but what explains the lack of anything with a standard deviation greater than 3 in either direction?

Do we need to have an explanation for that ?