Kent distribution

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The Kent Distribution was originally proposed as a spherical analogue of the normal distribution and serves as a natural extension to the vMF distribution. Used in spherical statistics, this probability distribution operates in the real three-dimensional coordinate space with a two-dimensional unit sphere.

Kent Distribution Definition

The Kent Distribution is a probability distribution derived from the 5-parameter Fisher-Bingham distribution. It’s a distribution designed to work in ℜ3, the real three-dimensional coordinate space, and operate on a two-dimensional unit sphere. It can be used in various fields, including neuroscience, computer graphics, computer vision, and geology. The Kent distribution is highly efficient, it can be an excellent option to model data in fields where rotation invariance is a major consideration.

The Kent distribution’s probability density function, (PDF), is given by

kent distribution pdf


  • γ1, γ1, γ1 are orthogonal unit vectors and represent the mean, major, and minor axes respectively [1];
  • κ measures the concentration,
  • 0 ≤ β < κ/2 describes the “ovalness,”
  • c(κ, β) is a normalizing constant, given by the equation
su normalizing constant
Iv(κ) represents the modified Bessel function.

Advantages of the Kent Distribution

The Kent Distribution has a couple of advantages that make it appealing to users. One significant benefit is that it provides an efficient way to model certain data sets. Its capability to create a rotationally invariant model allows it to be adequately applied in fields like computer vision and image processing. It can also be used in the analysis of fMRI data from the human brain due to rotations invariance, which can be used to model spherical coordinates.

The Kent Distribution has been widely used in numerous applications. In neuroscience, researchers have used the Kent distribution to model animal movement patterns to study their behavior in a particular environment. It has also been applied in computer vision to simulate the orientation of objects. Another application is in the field of geology where the Kent distribution has been used to analyze borehole data to build geological models.


[1] Kasarapu, P. (2015). Modelling of directional data using Kent distributions. Retrieved April 17, 2023 from:

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