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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

Information

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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