In
statistics, a bimodal distribution is a
continuous probability distribution with two different
modes. These appear as distinct peaks (local maxima) in the
probability density function, as shown in Figure 1.A good example is the height of a person. The heights of males form a roughly
normal distribution, as do those of females. Each of these distributions is unimodal. However, if we plot a single histogram of the entire population, we see two peaks—one for males and one for females.Bimodality is a property of many distributions. A bimodal distribution most commonly arises as a mixture of two different
unimodal distributions. In other words, the bimodally distributed random variable X is defined as with probability or with probability , where Y and Z are unimodal random variables and is a mixture coefficient. In the height example, Y would be the height of a random male, Z the height of a random female, and the probability that a random individual is male.
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A distribution that has two modes (thus two "peaks").
Bimodality of the distribution in a sample is often a strong indication that the distribution of the variable in population is not normal. Bimodality of the distribution may provide important information about the nature of the investigated variable (i.e., the measured quality). For example, if the variable represents a reported preference or attitude, then bimodality may indicate a polarization of opinions. Often however, the bimodality may indicate that the sample is not homogenous and the observations come in fact from two or more "overlapping" distributions. Sometimes, bimodality of the distribution may indicate problems with the measurement instrument (e.g, "gage calibration problems" in natural sciences, or "response biases" in social sciences).
See also
unimodal distribution ,
multimodal distribution .
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