Talk:Unimodal function
This page makes no sense to the non-mathematician. Someone should clean it up and make it easier to read. Also, wouldn't a parabola count? 216.165.95.5 06:56, 3 October 2007 (UTC)
Zero probability for x=m possible?
In probability and statistics, a "unimodal probability distribution" is a probability distribution whose probability density function is a unimodal function, or more generally, (...) (this allows for the possibility of a non-zero probability for x=m).
I don't understand. The second definition (more general) accepts P[x=m] > 0. This seems to imply that the first one does not. Then, as I understand it, the first definition only accepts as "unimodal probability distribution" a probability distribution whose pdf is a unimodal function of mode m, with P[x=m] = 0, that is, pdf(m)=0. Such a pdf can't be unimodal with mode m. And thus the first definition rejects every probability distribution of being unimodal and thus defines an empty concept...--OlivierMiR (talk) 18:19, 11 September 2008 (UTC)
Local maxima
Feller says that unimodal distribution is a distribution function that is convex up to the mode and concave beyond it. Thus it may have density taking maximal values on an interval (say uniform distribution on [0,1]). In this case all points in [0,1] are local maxima (or there aren't any, if we consider strict 'peaks' only). Therefore I suggest a more general definition of a unimodal function: a function whose local maxima make up an interval.
Moreover, it might be worth replacing '(this allows for the possibility of a non-zero probability for x=m)' with '(in this case the distribution may have density everywhere except, possibly, m; this allows for the possibility of a non-zero probability for x=m)'