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A Poincaré limit theorem for wrapped probability distributions on compact symmetric spaces

Published online by Cambridge University Press:  24 October 2008

P. E. Jupp
P. E. Jupp
Affiliation:
Department of Statistics, University of St Andrews
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Extract

In an article on the philosophy of chance, Poincaré[7] showed that the distribution of the stopping position of a needle pivoted about its centre tends to the uniform distribution on the circle as the distribution of the initial push becomes spread out along the real line. This result was formalized by Feller [2] and strengthened by Mardia [6] as follows.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 329 - 334
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Abraham, R.. Foundations of Mechanics. (Benjamin, 1967.)Google Scholar
[2]Feller, W.. An Introduction to Probability Theory and its Applications, vol. II (Wiley, 1966).Google Scholar
[3]Helgason, S.. Differential geometry, Lie groups, and symmetric spaces (Academic Press, 1978).Google Scholar
[4]Jupp, P. E. and Mardia, K. V.. Density-preserving statistics and densities for sample means. Ann. Probab. 6 (1978), 688–694.CrossRefGoogle Scholar
[5]Loos, O.. Symmetric Spaces, vol. II (Benjamin, 1969).Google Scholar
[6]Mardia, K. V.. Statistics of Directional Data. (Academic Press, 1972.)Google Scholar
[7]Poincaré, H.. Chance. Monist 22 (1912), 31–52.Google Scholar