Langevin distribution

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A distribution used to model spherical data. The probability density function f in the direction (θ, ϕ) (See spherical data) is given by

f(θ, ϕ)=c exp[κ{cosθ0 cosθ+sinθ0 sinθ cos(ϕ-ϕ0)}], 0≤θπ, -πϕ < π,

where c is a positive constant and the non-negative parameter κ is a measure of the concentration of the distribution, which is symmetrical about the mode. The case κ=0 corresponds to a uniform distribution over the entire sphere. If κ≠0 the distribution has mode at (θ0, ϕ0).

Subjects: Probability and Statistics.

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