The Kent distribution, also known as the 5-parameter Fisher-Bingham distribution, is a probability distribution in ℜ3, the real three dimensional coordinate space, of a two-dimensional unit sphere.
Kent Distribution PDF
The Kent distribution’s probability density function, f(x), is given by the equation:
- x is a three dimensional unit value.
- c(κ, β) is a normalizing constant, and is given by the equation
In the above equation, Iv(κ) represents what is called the modified Bessel function.
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Kent, J. T. (1982) The Fisher–Bingham distribution on the sphere., J. Royal. Stat. Soc., 44:71–80.
Mardia, K. V. M., Jupp, P. E. (2000) Directional Statistics (2nd edition), John Wiley and Sons Ltd