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yorwbatoday at 10:33 AM0 repliesview on HN

Assuming the measurements are independent samples from a normal distribution. Which they of course aren't, as measurements of adjacent days are obviously correlated (if they were independent, a 1-in-7000 event could be expected to happen on about 2 days within a 44-year span). Now the question is what the nature of the deviation is.

- How independent are measurements of different years?

- Has there been a systematic change in the distribution mean?

- Has there been a systematic change in the distribution variance?

- Was there a good reason to assume that the temperature distribution would be normally distributed to begin with? (Maybe there are strong non-additive effects.)

In any case, it's clear that assuming the observed temperatures in the 1991-2020 range follow a normal distribution and temperatures outside that date range will follow the same distribution is a bad model of reality.