Further to this, I don't think these U-shaped distributions (Yule's
term) are that extraordinary. One example used by Karl Pearson was
cloudiness. In some places the sky tends to be almost clear or almost
overcast most of the time and in between only occasionally. This isn't
true of Durham (that's Durham, UK, naturally). Any variable based on two
fairly stable states with occasional flips between them is likely to
behave quite similarly.
Karl Pearson. 1897.
Cloudiness: Note on a Novel Case of Frequency.
Proceedings of the Royal Society of London 62: 287-290.
Nick Cox
Quite so. The beta-distribution can indeed be U-shaped. Some people
would call that shape bimodal. Others define a mode as a peak with a
tail on either side, so that on such a stricter definition we have in
Maarten's case
two half-modes. (That doesn't make it unimodal!)
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