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On the infinite divisibility of the von Mises distribution

Published online by Cambridge University Press:  09 April 2009

Toby Lewis
Affiliation:
Department of Mathematical Statistics, The University, Hull, England.
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Abstract

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It is shown, by use of a Bochner-type condition for infinite divisibility, that the von Mises distribution is infinitely divisible for some values of the concentration parameter k, certainly for k < 0.16.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

Grenander, U. and Szegö, G. (1958), Toeplitz Forms and their Applications (University of California Press, Berkeley and Los Angeles, 1958).CrossRefGoogle Scholar
Johansen, S. (1966), ‘An application of extreme point methods to the representation of infinitely divisible distributions’, Z. Wahrscheinlichkeitstheorie verw. Geb. 5, 304316.CrossRefGoogle Scholar
Kendall, M. G. and Stuart, A. (1968), The Advanced Theory of Statistics, Vol. 3 (Griffin, London, 1968).CrossRefGoogle Scholar
Lewis, T. (1975), ‘Probability functions which are proportional to characteristic functions and the infinite divisibility of the von Mises distribution’, contribution to Perspectives in Probability and Statistics (Papers in Honour of M. S. Bartlett on the Occasion of his Sixty-Fifth Birthday) ed. Gani, J. (Academic Press, London), 1928.Google Scholar
Mardia, K. V. (1972), Statistics of Directional Data (Academic Press, London and New York, 1972).Google Scholar
Wold, H. (1954), A Study in the Analysis of Stationary Time Series (Almqvist and Wiksell, Stockholm, 2nd edition, 1954).Google Scholar