Trimodal

Trimodal refers to a distribution or data set that exhibits three distinct modes, or local maxima, in its probability density function or empirical histogram. A mode is a point where the density is locally highest; a trimodal distribution therefore has three separated peaks, with regions of relatively lower density between them.

Trimodality can arise when the data come from a mixture of three subpopulations, each contributing its own peak, or from a process with three characteristic states. It is commonly modeled by finite mixture distributions, such as a mixture of three normal components, though other shapes are possible. Trimodality can also result from scale or boundary effects, or from combining data from different sources. Interpretations should consider whether peaks reflect genuine subgroups or artifacts of data collection, transformation, or sample size.

Detection and inference methods include graphical inspection with histograms and kernel density estimates, which reveal multiple peaks. Formal tests for multimodality include Silverman’s test and the dip test, often employed with bootstrap methods. Model-based approaches fit finite mixture models and use information criteria to determine the number of components, providing a probabilistic framework for identifying three modes.

In practice, trimodality signals potential substructure in the data, suggesting the need for further analysis to understand underlying subpopulations or processes.