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Limiting behaviour of the von Mises-Fisher distribution

Published online by Cambridge University Press:  24 October 2008

John Kent
John Kent
Affiliation:
University of Leeds
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Abstract

The von Mises-Fisher density of parameter K is shown to be very similar to the spherical normal distribution of parameter υ = 1/K as k → ∞. In fact the two densities are closer by factor of K than one might expect.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 3 , November 1978 , pp. 531 - 536
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Erdélyi, A., Magnus, W., Oberhettingr, F. and Tricomi, F. G.Bateman Manuscript Project, higher transcendental functions, vol. II (New York; McGraw-Hill, 1953).Google Scholar
(2)Hartman, P.Completely monotone families of solutions of n-th order linear differential equations and infinitely divisible distributions, Ann. Scuola Norm. Sup. Pisa series iv, 3 (1976), 267–287.Google Scholar
(3)Hartman, P. and Watson, G. S.‘Normal’ distribution functions on spheres and the modified Bessel functions. Ann. Prob. 2 (1974), 593–607.CrossRefGoogle Scholar
(4)Kent, J.The infinite divisibility of the von Mises-Fisher distribution for all values of the parameter in all dimensions. Proc. London Math. Soc. (3) 35 (1977), 359–384.CrossRefGoogle Scholar