Summary
In a previous paper [4], the author has derived the distribution of the length of the projection of a random unit vector inR n on the subspaceR m (1≦mň). The method used there is now applied to a direction defined by a unit vector of ann-dimensional hypersphere on the surface of which the probability element is given by then-dimensional von Mises distribution. The results obtained here include the previous results as a special case, since the random direction is a special case of von Mises direction.
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References
Abramowitz, Milton and Stegan, Irene A. (1965) (editors).Handbook of Mathematical Functions with formulas, graphs and mathematical tables, Dover Publications Inc., New York, p. 376.
Downs, T. D. (1966). Some relationships among the von Mises distributions of different dimensions,Biometrika,53, 269–272.
Feller, W. (1966).An Introduction to Probability Theory and Its Applications, Vol. II, John Wiley & Sons Inc., New York, 29–33.
Lwin, T. (1970). On random directions, (paper submitted tothe Aust. Jour. Statist.).
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Lwin, T. On von mises directions. Ann Inst Stat Math 27, 79–86 (1975). https://doi.org/10.1007/BF02504626
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DOI: https://doi.org/10.1007/BF02504626