extreme value statistics [View All]

I've been thinking about extreme value statistics recently.

If you repeatedly sample from a random variable, the (expected) time between achieving successive maximums grows exponentially. For example, here's some results I got from repeatedly sampling from a Normal distribution of standard deviation (1). Each number is the average number of trials to beat the previous maximum value:

{9.009, 61.989, 365.096, 1560.31, 4906.24}

If you plot these, you get a nice exponential curve. This is true for pretty much any distribution that's applied out in the "real world."

Why am I posting this in E/E? Consider climate change measurements. In the null-hypothesis that climate change isn't happening, we would expect weather "records" to be broken less and less frequently over time. In fact, the time between records would grow exponentially.

But that isn't what we're seeing. Weather records are broken on a fairly regular basis. The time between record-breakers appears to be constant, or maybe even accelerating.

And then there is the nature of the records themselves. In the "constant-climate" scenario (null-hypothesis), each time a record is broken, it's expected difference is less: the record is broken by a more narrow margin each time. Here are the differences between each maximum and the previous maximum:

{0.902897, 0.597499, 0.490741, 0.403293, 0.353109}

As we've seen in the last year, old weather records aren't just being broken, they are being smashed. 27 tropical storms. 143 days without rain.

I think that there are other statistical methods that are better for approaching these questions scientifically, but I thought it was interesting, since as humans we tend to be tuned in to extraordinary events, as opposed to less flashy statistical analysis.