Abstract
The Langevin (or von Mises-Fisher) distribution of random vector x on the unit sphere ω q in R q has a density proportional to exp κμ'x where μ'x is the scalar product of x with the unit modal vector μ and κ ⩾0 is a concentration parameter. This paper studies estimation and tests for a wide variety of situations when the sample sizes are large. Geometrically simple test statistics are given for many sample problems even when the populations may have unequal concentration parameters.
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