unimodal

Unimodal means having a single mode. In statistics and probability, a unimodal distribution has a single local maximum in its probability density or mass function, corresponding to a single most probable value or interval.

The concept contrasts with multimodal distributions, which have two or more distinct peaks, and with uniform distributions which are not considered unimodal because there is no single peak. The mode can be interior or at a boundary depending on the shape and domain.

Examples: The normal distribution is the canonical unimodal distribution with a symmetric single peak. The Poisson distribution is unimodal for all lambda > 0, with a mode at floor(lambda). The exponential distribution is unimodal with its mode at 0. The binomial distribution is unimodal for 0<p<1, with mode floor((n+1)p). Some Beta or t distributions may be unimodal depending on parameters.

In function analysis, a real-valued function on an interval is called unimodal if it has one peak and is nonincreasing to the left of the peak and nondecreasing to the right (or vice versa). Unimodality is a weaker condition than strict concavity and is connected to optimization and economic theory.

In data analysis, assessing unimodality helps choose modeling techniques; there are statistical tests and methods to evaluate whether a sample is unimodal or multimodal, such as visual inspection, kernel density estimates, and Silverman's test.