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A classification theorem for planar distributions based on the shape statistics of independent tetrads

Published online by Cambridge University Press:  24 October 2008

Christopher G. Small
Christopher G. Small
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ont. N2L 3Gl, Canada
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Extract

The uniformity of a certain shape density of a random ΠD tetrad relative to Lebesgue measure along part of the set corresponding to alignment is shown to be sufficient under certain technical conditions for the generating distribution to be the uniform distribution on a compact convex set. A counter-example is provided to show that this result fails for random IID triangles. The main theorem is used to characterize circular, elliptical and triangular uniform generators from the shape distribution of random IID tetrads.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 3 , November 1984 , pp. 543 - 547
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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