Unimodality - Unimodal Probability Distribution

In statistics, a unimodal probability distribution (or when referring to the distribution, a unimodal distribution) is a probability distribution which has a single mode. As the term "mode" has multiple meanings, so does the term "unimodal".

Strictly speaking, a mode of a discrete probability distribution is a value at which the probability mass function (pmf) takes its maximum value. In other words, it is a most likely value. A mode of a continuous probability distribution is a value at which the probability density function (pdf) attains its maximum value. Note that in both cases there can be more than one mode, since the maximum value of either the pmf or the pdf can be attained at more than one value.

If there is a single mode, the distribution function is called "unimodal". If it has more modes it is "bimodal" (2), "trimodal" (3), etc., or in general, "multimodal". Figure 1 illustrates normal distributions, which are unimodal. Other examples of unimodal distributions include Cauchy distribution, Student's t-distribution and chi-squared distribution. Figure 2 illustrates a bimodal distribution.

Figure 3 illustrates a distribution which by strict definition is unimodal. However, confusingly, and mostly with continuous distributions, when a pdf function has multiple local maxima it is common to refer to all of the local maxima as modes of the distribution. Therefore, if a pdf has more than one local maximum it is referred to as multimodal. Under this common definition, Figure 3 illustrates a bimodal distribution.