A Gaussian distribution can have a standard deviation not much smaller than its mean
That’s true of Gaussians in general, but Gaussians obtained as the limiting distribution of binomial random events will have a standard deviation roughly equal to the square root of the mean. In this case, looking at the data you linked to, the mean would be about 30 for a stdev=5.5, so an observation of X=60 would be a 5-sigma Black Swan.
Indeed the last 8 counts of annual US lightning fatalities vary over a range of a factor of 2.
You’re misinterpreting this data. What’s happening is a overall decrease in the probability of getting struck by lightning, (which probably has to do with urbanization), not statistical fluctuation. If you don’t believe me, I’ll give you 10:1 odds that the number of lightning deaths in 2015 is less than 60 :-)
That’s true of Gaussians in general, but Gaussians obtained as the limiting distribution of binomial random events will have a standard deviation roughly equal to the square root of the mean.
Good point.
In this case, looking at the data you linked to, the mean would be about 30 for a stdev=5.5, so an observation of X=60 would be a 5-sigma Black Swan.
True enough, though the factor-of-2 fluctuation I had in mind was more like a jump from 23 to 45 (2013′s & 2007′s numbers respectively), and those values are more like 2.2-sigma & 1.7-sigma events (using the observed 2006-2013 average as the parameter of a Poisson distribution). Still pretty unlikely, of course.
You’re misinterpreting this data. What’s happening is a overall decrease in the probability of getting struck by lightning, (which probably has to do with urbanization), not statistical fluctuation.
Yeah, you’re right. (Well, I disagree about the urbanization explanation, the dip looks too sudden. But other than that.) If I take the 2006-2013 figures, subtract their mean μ from each of them and divide the results by √μ, that should give me z-scores (if the data are IID & Poisson). The sum of those z-scores’ squares should then be roughly χ²-distributed with n − 1 = 7 degrees of freedom, but the actual χ² statistic I get is too far in the tail for that to be plausible (χ² = 17.9, hence p = 0.012). So the lightning deaths are unlikely to be IID from a Poisson (or, nearly equivalently, Gaussian) distribution.
That’s true of Gaussians in general, but Gaussians obtained as the limiting distribution of binomial random events will have a standard deviation roughly equal to the square root of the mean. In this case, looking at the data you linked to, the mean would be about 30 for a stdev=5.5, so an observation of X=60 would be a 5-sigma Black Swan.
You’re misinterpreting this data. What’s happening is a overall decrease in the probability of getting struck by lightning, (which probably has to do with urbanization), not statistical fluctuation. If you don’t believe me, I’ll give you 10:1 odds that the number of lightning deaths in 2015 is less than 60 :-)
Good point.
True enough, though the factor-of-2 fluctuation I had in mind was more like a jump from 23 to 45 (2013′s & 2007′s numbers respectively), and those values are more like 2.2-sigma & 1.7-sigma events (using the observed 2006-2013 average as the parameter of a Poisson distribution). Still pretty unlikely, of course.
Yeah, you’re right. (Well, I disagree about the urbanization explanation, the dip looks too sudden. But other than that.) If I take the 2006-2013 figures, subtract their mean μ from each of them and divide the results by √μ, that should give me z-scores (if the data are IID & Poisson). The sum of those z-scores’ squares should then be roughly χ²-distributed with n − 1 = 7 degrees of freedom, but the actual χ² statistic I get is too far in the tail for that to be plausible (χ² = 17.9, hence p = 0.012). So the lightning deaths are unlikely to be IID from a Poisson (or, nearly equivalently, Gaussian) distribution.