# Unimodal function

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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*).

In probability and statistics, a **unimodal probability distribution** is a probability distribution where the probability density function is a unimodal function. For a unimodal probability distribution of a continuous random variable, the Vysochanskiï-Petunin inequality provides a refinement of the Chebyshev inequality.

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