In directional statistics, the Kent distribution, also known as the 5-parameter Fisher–Bingham distribution (named after John T. Kent, Ronald Fisher, and Christopher Bingham), is a probability distribution on the unit sphere (2-sphere S2 in 3-space R3). It is the analogue on S2 of the bivariate normal distribution with an unconstrained covariance matrix. The Kent distribution was proposed by John T. Kent in 1982, and is used in geology as well as bioinformatics.

Definition

The probability density function of the Kent distribution is given by:

is:

is the modified Bessel function is the gamma function, the normalizing constant of the Von Mises–Fisher distribution.

must be orthogonal.

Generalization to higher dimensions

-dimensional Kent distribution is proportional to

.

See also

• Directional statistics

• Von Mises–Fisher distribution

• Bivariate von Mises distribution

• Von Mises distribution

• Bingham distribution

References

• Boomsma, W., Kent, J.T., Mardia, K.V., Taylor, C.C. & Hamelryck, T. (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.

• Hamelryck T, Kent JT, Krogh A (2006) Sampling Realistic Protein Conformations Using Local Structural Bias. PLoS Comput Biol 2(9): e131

• Kent, J. T. (1982) The Fisher–Bingham distribution on the sphere., J. Royal. Stat. Soc., 44:71–80.

• Kent, J. T., Hamelryck, T. (2005). Using the Fisher–Bingham distribution in stochastic models for protein structure . In S. Barber, P.D. Baxter, K.V.Mardia, & R.E. Walls (Eds.), Quantitative Biology, Shape Analysis, and Wavelets, pp.57–60. Leeds, Leeds University Press.

• Mardia, K. V. M., Jupp, P. E. (2000) Directional Statistics (2nd edition), John Wiley and Sons Ltd.

• Peel, D., Whiten, WJ., McLachlan, GJ. (2001) Fitting mixtures of Kent distributions to aid in joint set identification. J. Am. Stat. Ass., 96:56–63