unimodale

Unimodale is the Italian term for unimodal, a concept used in statistics to describe a probability distribution that has a single mode. A mode is a point or region where the distribution’s density (for continuous distributions) or probability mass (for discrete distributions) is maximally high. A unimodal distribution typically increases up to its peak and then decreases, though some definitions allow a plateau at the top.

In practice, not all distributions are unimodal. Multimodal distributions exhibit multiple distinct peaks. Edge cases exist: the uniform distribution often has a flat top across its support and is not universally regarded as unimodal; some discrete distributions with specific parameter values may produce two or more modes.

Examples commonly cited as unimodal include the normal distribution, which is the canonical case, the exponential distribution (with its single mode at the origin), and gamma distributions with shape greater than one. Beta distributions can be unimodal for many parameter choices, while others are U-shaped or bimodal depending on the parameters.

Assessing unimodality involves both visual and formal approaches. Visual tools include histograms and kernel density estimates to identify the number of peaks. Formal tests for unimodality include Hartigan’s dip test and Silverman’s test, which aim to determine whether the data are better described by a single mode or multiple modes. When unimodality is in doubt, fitting mixture models can help identify potential multiple components.

See also: multimodality, bimodality, density estimation, mode, Hartigan’s dip test, Silverman’s test.