bimodality

Bimodality is a property of a probability distribution characterized by two distinct local maxima, or modes, in its density or frequency plot. A mode is a point where the distribution is locally most frequent. A distribution with exactly two such peaks is bimodal; if there are more than two peaks it is multimodal, and if there is a single peak it is unimodal.

Bimodality often arises when the data come from two or more subpopulations with different characteristics, such as a mixture of two normal distributions with different means. Other causes include natural dichotomies in the process, phase transitions, or measurement artifacts that split observations into two groups. If data are discretized or heavily rounded, artificial bimodality can also appear.

Detecting bimodality typically involves visual inspection of histograms or kernel density estimates. Statistical tests include Hartigan's dip test for unimodality and Silverman's test for the number of modes. A commonly cited heuristic is the bimodality coefficient, B = (gamma^2 + 1)/kurtosis, where gamma is skewness and kurtosis is the excess kurtosis; values above about 0.55 suggest bimodality.

Interpretation and analysis: Bimodality indicates heterogeneity in the data and may motivate modeling with mixtures, clustering, or stratified analyses by subpopulation. It can affect inference and prediction if a single-model assumption is inappropriate. Examples include gene-expression data with "on" and "off" states, height or income distributions in mixed sexes or age groups, and customer behavior with two preferred purchase levels.