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 (i.e. there is one mode as the name indicates).
Examples of unimodal functions:
A function f(x) is "Sunimodal" if its Schwartzian derivative is negative for all .
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 nonzero probability for x=m). For a unimodal probability distribution of a continuous random variable, the VysochanskiiPetunin inequality provides a refinement of the Chebyshev inequality. Compare multimodal distribution.
In computational geometry if a function is unimodal it permits the design of efficient algorithms for finding the extrema of the function.^{[1]}
