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Unimodal function
From Wikipedia, the free encyclopedia
In mathematics, a function f(x) between two ordered sets is unimodal if for some value m (the mode), it is monotonically increasing for x ≤ m and monotonically decreasing for x ≥ m. In that case, the maximum value of f(x) is f(m) and there are no other local maxima.
Examples of unimodal function:
Function 
is S-unimodal if its Schwartzian derivative is negative for all 
[1].
In probability and statistics, a unimodal probability distribution is a probability distribution whose probability density function is a unimodal function, or more generally, whose cumulative distribution function is convex up to m and concave thereafter (this allows for the possibility of a non-zero probability for x=m). For a unimodal probability distribution of a continuous random variable, the Vysochanskii-Petunin inequality provides a refinement of the Chebyshev inequality. Compare multimodal distribution.
- ^ http://web.udl.es/usuaris/y4370980/abstracts/abstracts/vol-42/de_melo.pdf W. De Melo : Bifurcation of Unimodal Maps Qualitative Theory of Dynamical Systems VOLUME 4 - Number 2 (pages 413-424)