Probability Distributions > Kent distribution

The **Kent distribution**, also known as the *5-parameter Fisher-Bingham distribution*, is a probability distribution in ℜ^{3}, 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:

Here,

- x is a three dimensional unit value.
- c(κ, β) is a normalizing constant, and is given by the equation

In the above equation, I_{v}(κ) represents what is called the modified Bessel function.

## References

Boomsma, W., et al. (2006) Graphical models and directional statistics capture protein structure. In S. Barber, P.D. Baxter, K.V.Mardia, & R.E. Walls (Eds.), Interdisciplinary Statistics and Bioinformatics, pp. 91–94. Leeds, Leeds University Press.

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