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On the induced distribution of the shape of the projection of a randomly rotated configuration

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

H. Le  and
D. Barden
H. Le*
Affiliation:
University of Nottingham
D. Barden*
Affiliation:
University of Cambridge
*
∗ Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK. Email address: [email protected]
∗∗ Postal address: DPMMS, University of Cambridge, Wilberforce Road, Cambridge, CB3 OWB, UK.
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Abstract

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Using the geometry of the Kendall shape space, in this paper we study the shape, as well as the size-and-shape, of the projection of a configuration after it has been rotated and, when the given configuration lies in a Euclidean space of an arbitrary dimension, we obtain expressions for the induced distributions of such shapes when the rotation is uniformly distributed.

Keywords

Kendall shape spaceshapesize-and-shapehorizontal liftRiemannian submersion

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 42 , Issue 2 , June 2010 , pp. 331 - 346
Copyright
Copyright © Applied Probability Trust 2010 

References

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