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Some new integral geometric formulae, with stochastic applications

Published online by Cambridge University Press:  14 July 2016

R. E. Miles
R. E. Miles*
Affiliation:
The Australian National University
*
∗ Postal address: Research School of Social Sciences, Department of Statistics, IAS, The Australian National University, P.O.Box 4, Canberra, ACT 2600, Australia.
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Abstract

Alternative forms of the integral geometric density of an r-subspace [r-flat] containing q[q + 1] points in euclidean n-space Rn are given Stochastic applications in R3 include formulae for

(i) the mean area of intersection of a domain by an isotropic plane through the origin; and

(ii) the variance of the area of intersection of a domain by an isotropic uniform plane.

Keywords

GEOMETRICAL PROBABILITYINTEGRAL GEOMETRYINVARIANT DENSITYBLASCHKE–PETKANTSCHIN FORMULAISOTROPIC RANDOM SUBSPACEISOTROPIC UNIFORM RANDOM FLATMEAN PROJECTIONRANDOM SECANTCONVEX SETCROFTON'S FORMULARANDOM SIMPLEX
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 592 - 606
Copyright
Copyright © Applied Probability Trust 1979 

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