Unimodal Function
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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). In probability and statistics, a "unimodal probability distribution" is a probability distribution whose probability density function is a unimodal function, or m...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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). 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. In computational geometry if a function is unimodal it permits the design of efficient algorithms for finding the extrema of the function.
