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The volume of an isotropic random parallelotope

Published online by Cambridge University Press:  14 July 2016

Harold Ruben
Harold Ruben*
Affiliation:
McGill University
*
∗Postal address: Department of Mathematics, McGill University, 805 Sherbrooke St. W., Montreal, P.Q. Canada, H3A 2K6.
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Abstract

The p-content of the p-parallelotope ∇p, n determined by p independent isotropic random points z1, …, zp in ℝn (1 < p ≦ n) can be expressed as a product of independent variates in two ways, by successive orthogonal projection onto linear subspaces and by radial projection of the points, enabling calculation of the actual distribution as well as the moments of ∇p, n. This is done explicitly in several cases. The results also have interest in multivariate statistics.

Keywords

CONTENT OF RANDOM ISOTROPIC RANDOM PARALLELOTOPEORTHOGONAL AND RADIAL PROJECTIONPRODUCT EXPRESSIONS FOR CONTENTGENERALIZED SINE
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 84 - 94
Copyright
Copyright © Applied Probability Trust 1979 

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References

[1] Anderson, T. W. (1958) An Introduction to Multivariate Statistical Analysis. Wiley, New York.Google Scholar
[2] Johnson, N. L. and Kotz, S. (1972) Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York.Google Scholar
[3] Kelker, D. (1970) Distribution theory of spherical distributions and a location-scale parameter generalization. Sankhya A 32, 419–430.Google Scholar
[4] Kendall, M. G. and Stuart, A. (1960) The Advanced Theory of Statistics, Vol. 2. Hafner Press, New York.Google Scholar
[5] Miles, R. E. (1971) Isotropic random simplices. Adv. Appl. Prob. 3, 353–382.CrossRefGoogle Scholar
[6] Sommerville, D. M. Y. (1929) An Introduction to the Geometry of N Dimensions. Methuen, London.Google Scholar