Kent distribution

The 5-parameter Fisher–Bingham distribution or Kent distribution, named after Ronald Fisher, Christopher Bingham, and John T. Kent, is a probability distribution on the two-dimensional unit sphere ${\displaystyle S^{2}\,}$ in ${\displaystyle {\mathbb {R}}^{3}}$ . It is the analogue on the two-dimensional unit sphere of the bivariate normal distribution with an unconstrained covariance matrix. The distribution belongs to the field of directional statistics. The Kent distribution was proposed by John T. Kent in 1982, and is used in geology as well as bioinformatics.

The probability density function ${\displaystyle f(\mathbf {x} )\,}$ of the Kent distribution is given by:

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