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The Wikipedia site for Multimodal Distributions states "Important bimodal distributions include the arcsine distribution and the beta distribution". I thought the beta distribution is unimodal.

ColorStatistics
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    What do you observe when you make a plot of a beta distribution with both parameters less than 1? The wikipedia article for the beta distribution even includes a plot showing bimodality https://en.wikipedia.org/wiki/Beta_distribution Some discussion: https://stats.stackexchange.com/questions/362728/whats-the-intuition-for-a-beta-distribution-with-alpha-and-or-beta-less-than – Sycorax Jul 13 '22 at 19:50
  • Oh, yeah; got it, thanks but to call it bimodal when it is bimodal for only 0.001% of its possible alpha, beta parameters seems like a bit of a misnomer. Khrushke, in his book, for example calls the beta distribution unimodal and that seems to be closer to the truth except for the 1 technicality you mention (both alpha and beta are exceedingly small <0.1). – ColorStatistics Jul 13 '22 at 19:58
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    Technically, that's zero percent of all possible parameter values. If Krushke really does assert Beta distributions are unimodal, that would be just as misleading as asserting they are bimodal. – whuber Jul 13 '22 at 20:00
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    Ok, revisited Khruske... my mistake... he shows a particular bimodal distribution with the modes not at the edges and says that there is no beta distribution to model it; he is correct; my fault. Thank you all for the clarifications. – ColorStatistics Jul 13 '22 at 20:04

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A Beta distribution need not be bimodal, but it absolutely can be. When the parameters both are less than $1$, then there is bimodality.

I would have phrased it more like "arcsine distribution (name given to Beta(1/2, 1/2)) and other beta distributions that have both parameters less than $1$".

Dave
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    That's superfluous: the so-called arcsine distribution is the Beta$(1/2,1/2)$ distribution. In the original context that is a big hint about the writer's meaning. – whuber Jul 13 '22 at 20:02