# Bipolar Distribution

A bipolar distribution is a specific type of bimodal distribution that has two distinct peaks offering contradictory information. In some cases, the term may also refer to the Watson bipolar distribution. The term is commonly found in biology to describe the distribution of species at both poles.

## Bimodal vs. Bipolar Distribution

The following image shows a bipolar distribution of movie ratings where movie goers either hate or love the movie [1]. As such, it offers a wealth of contradictory information; while we know everyone hated or loved the movie, we cannot make any determination at all about the quality of the movie.

This distribution can also be described as an extreme U-shaped distribution [3].

In contrast, a bimodal distribution is a distribution with two distinct peaks or modes. The modes can be anywhere on the distribution.

The above image shows two peaks at 3 and 8: that tells us the bulk of students get either three or eight answers right, with a variety of other possibilities. The graph provides a little information (but not much) about the quality of the test or student performance.

## Bipolar distribution in biology

In biology, a “bipolar distribution” refers to the presence of species in the Northern and Southern hemispheres. For example, species of marine bacteria are found exclusively at both poles and nowhere else [4]. Many marine species such as anchovies, saury, and gray dolphin are found near the poles but are absent in the tropics [5].

## Watson bipolar distribution

The Watson bipolar distribution  (or simply the Watson distribution) is a single-direction distribution used in directional data analysis, where bipolar or girdle distribution are required [2]; Girdle distributions are measurement bands on the stereographic projection, scattered on the sides of a great circle [6].

## References

[1] STAT 22000 Lecture Slides Variability in Estimates & Central Limit Theorem. http://www.stat.uchicago.edu/~yibi/teaching/stat220/17aut/Lectures/L14.pdf

[2] Mardia, K. V., & Dryden, I. L. (1999). The Complex Watson Distribution and Shape Analysis. Journal of the Royal Statistical Society. Series B (Statistical Methodology)61(4), 913–926. http://www.jstor.org/stable/2680713

[3] Klein, Ingo, 2017. “(Generalized) maximum cumulative direct, paired, and residual Φ entropy principle,” FAU Discussion Papers in Economics 25/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics

[4] Sul et al. January 16, 2013. Marine bacteria exhibit a bipolar distribution. Retrieved April 22, 2023 from: https://www.pnas.org/doi/10.1073/pnas.1212424110

[5] Sverdrup, H. (1942). The Oceans Their Physics, Chemistry, and General Biology. XVIIAnimals in Relation to Physical-Chemical Properties of the Environment. Prentice-Hall.

[6] Waldron, J. (2020). Data in Structural Geology. https://courses.eas.ualberta.ca/eas421/lecturepages/orientation.html

Scroll to Top