If X people died from lightning in 2014, then it is very unlikely that 2X people will die from lightning in 2015,
This doesn’t actually follow from (annual?) lightning strikes being nearly Gaussian. A Gaussian distribution can have a standard deviation not much smaller than its mean, in which case a fall of 50% or a rise of 100% from one year to the next wouldn’t be so unlikely. Indeed the last 8 counts of annual US lightning fatalities vary over a range of a factor of 2.
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.
This doesn’t actually follow from (annual?) lightning strikes being nearly Gaussian. A Gaussian distribution can have a standard deviation not much smaller than its mean, in which case a fall of 50% or a rise of 100% from one year to the next wouldn’t be so unlikely. Indeed the last 8 counts of annual US lightning fatalities vary over a range of a factor of 2.
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.