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)


 * This is an extremely common problem with many, many mathematics-related articles in Wikipedia - perhaps hundreds or even thousands of articles. I have a certain interest in mathematics, but little technical knowledge, and I sometimes come across mathematical terms in other articles and follow the link to find out more, only to back out immediately upon realizing I don't have a hope of understanding the mathematical article - even the brief introductory paragraph.  The article may contain a dozen technical terms, each of them a link to another article; but when you visit each of the following articles, it itself contains a dozen links to yet other terms - and so it multiplies exponentially for who knows how long.  It would take months to follow up all these links and understand them, and probably few people have the time to do that.


 * This may not be the best place to make the suggestion, but I don't know where to make it: but I would like to see an overall campaign in Wikipedia, covering all mathematical articles, to make them understandable to non-mathematicians.


 * I don't think the technical information should be removed or thinned out, as it may be genuinely useful to mathematically-knowledgeable readers. I am not saying these sections should be rewritten at all - but that an easier-to-understand summary should be provided at the top of these articles.  As far as I can tell, a huge section of Wikipedia's mathematics-related content is just completely inaccessible to non-mathematicians.


 * Perhaps mathematics articles, or indeed any highly technical article, could have two major sections: an introductory section which is intended to make the topic as understandable as possible to a non-specialist - and then a further (probably much longer) section, very detailed, which can contain all the technical information in the world. I want to emphasize that my idea is to *add* content (the easier-to-understand sections), not to remove content (the technical information).


 * In some cases, even a three-tiered approach may work, the middle tier being a section of intermediate detail which may require (for example) a knowledge of high-school mathematics but no more. (That would be understandable by myself, for example, whereas the very technical articles are not.)


 * Any thoughts on this? M.J.E. (talk) 09:14, 1 March 2010 (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)'

Matumba (talk) 17:56, 17 March 2009 (UTC)

Pascal's triangle
I removed Pascal's triangle as an example since it does not follow the strict definition given here. The definition talks about "monotonically increasing for x ≤ m and monotonically decreasing for x ≥ m". In Pascal's triangle it is "monotonically non-decreasing for x ≤ m and monotonically non-increasing for x ≥ m", that is, a value can repeat. Specifically, in the page Pascal's triangle one can see the 3rd line has 3 twice. The value is not increasing or decreasing. What one can do is add a weaker form for which it applies. I might do that, but I want to check first. For now I removed the misleading example. --Muhandes (talk) 17:27, 6 July 2010 (UTC)

Redirect to unimodal
Rather than try to rewrite both this page and unimodal distribution I wrote unimodal and redirected there. I hope this is better solution. If not you are free to revert. --Muhandes (talk) 18:15, 12 July 2010 (UTC)