Kent distribution

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

Where

• 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