User talk:BigBendRegion

Please elaborate on the Finucan conditions. I was not able to find any references. Zechmann2 (talk) 19:24, 3 February 2020 (UTC)

Answer: They are described in here:

http://www.mriquestions.com/uploads/3/4/5/7/34572113/kurtosis_statistician.pdf

They show sufficient conditions for kurtosis to increase that involve increased probability in the tail. Importantly, these are not *necessary* conditions, so it is also possible to have increased kurtosis with less probability in the tail, provided that the tail extends farther.

What is absolutely, mathematically true is that when one distribution has higher kurtosis than another, then there is greater tail weight, where tail weight (more properly stated, *leverage*) is determined by the fourth powers of the standardized variable. See here, for example: https://math.stackexchange.com/a/3532888/472987

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Another issue brought up in some recent revisions is that kurtosis is only associated with tail weight rather than a direct measure of tailweight. The reason kurtosis is a direct measure is shown in https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4321753/. Therein, the specific tailweight measure is defined, and three theorems establishing the closeness of kurtosis to that measure are proven.

See also https://math.stackexchange.com/a/3532888/472987, which shows mathematically that if one distribution has higher kurtosis than another, then it must have greater tailweight, not greater central mass or peakedness.