< Probability distribution list < Bimodal distribution
A bimodal distribution has two modes that may or may not be symmetric [2].
Most probability distributions has one peak, which happens around the mean or median [3]. For example, a bell curve typically shows concentration of observations, typically around the mean. However, a bimodal distribution has two distinct peaks – showing that data points are distributed across two separate values.
A mode indicates there is a single most common number within a set of data points, the “mode” in a bimodal distribution identifies two local maximums — where values stop trending up and start trending down. The mean and median lie between the two peaks and are not near either one [3].
The “bi” in bimodal distribution comes from the Latin bis, which means two. “Modal” refers to the peaks.
What a Bimodal Distribution tells you
- Two peaks may indicate two different groups [2]. For example:
- Exam scores often have a single peak, indicating that students are of similar ability. However, bimodal distributions can appear in grades sometimes – with many getting As and Fs – which suggests two distinct groups at play. This may be evidence of one group being more prepared than the other: either due to a lack or surplus of prior knowledge.
- A bimodal distribution might result from a natural process such as the breakup of large particles, multiple sources of particles or variable growth mechanisms in a system [4]. In climatology, the Lifetime Maximum Intensity (LMI) distribution of tropical cyclones (defined as the peak one-minute maximum sustained wind achieved by a tropical cyclone during its lifetime) is bimodal, which means that major storms are not very rare compared to less intense storms [6] — although there is no consensus on why this bimodality occurs. [7].
- Two peaks could also indicate your data is sinusoidal (wave-like). If you suspect your data might be following a wave-like pattern, create a scatter or run sequence plot to double-check for sinusoidal patterns. If the data points form a wave-like pattern, this would be a strong indication that the data is sinusoidal. If data is smooth with regular frequency and is symmetrical, that also indicates a sinusoidal pattern:
- Peaks and troughs occur at regular intervals.
- Peaks and troughs are of equal height (i.e., symmetrical).
- Data is smooth, with no sudden jumps or changes in the data.
- Sometimes, what looks like a bimodal distribution might be two unimodal distributions. For example, this following image shows two separate distributions graphed on the same axes.
A mixture of two normal distributions will not be bimodal unless there is a large difference between their means — typically bigger than the sum of the individual distribution’s standard deviations [5].
References
[1] Qwfp at English Wikipedia, CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0, via Wikimedia Commons
[4] Particle Size Distribution Functions:
[5] Schilling, M. et al. (2002). Is Human Height Bimodal? The American Statistician, Vol. 56, No. 3, (Aug., 2002), pp. 223-229
[6] Lee, C. et al. (2015) Rapid intensification and the bimodal distribution of tropical cyclone intensity. Nature Communications. DOI: 10.1038/ncomms10625
[7] Kim, S. et al. Decision-Tree-Based Classification of Lifetime Maximum Intensity of Tropical Cyclones in the Tropical Western North Pacific