Summary
The distributions of ray and secant lengths through arbitrary convex bodies for five different randomness measures has previously been obtained. This article concentrates on the ray and secant moment relationships that exist among these various measures. In particular various moments depend only on the volume and surface concent of the n-dimensional convex body. Specific moment relationships have been obtained for regular convex bodies which include all n-dimensional regular polyhedra. The result will be illustrated by applications.
The Author acknowledges the support of the National Science and Engineering Research Council of Canada.
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References
Coleman, R. (1969). Random paths through convex bodies. Journal of Applied Probability, 6, 430–441.
Coleman, R. (1973). Random paths through rectangles and cubes. Metallograph, 6, 103–114.
Ehlers, P.F. (1972). Particle number fluctuations and geometrical probability. Ph.D. Thesis, University of British Columbia.
Enns, E.G., Ehlers, P.F. (1978). Random paths through a convex region. Journal of Applied Probability, 15, 144–152.
Enns, E.G., Ehlers, P.F. (1980). Random paths originating within a convex region and terminating on its surface. Australian Journal of Statistics, to appear in April.
Enns, E.G., Ehlers, P.F. (1980). Random secants of a convex body generated by surface randomness. Journal of Applied Probability, to appear.
Hadwiger, H. (1950). Neue Integralrelationen für Eikörperpaare. Acta Scientiarum Mathematicarum, 13, 252–257.
Kellerer, A.M. (1971). Considerations on the random transversal of convex bodies and solutions for general cylinders. Radiation Research, 47, 359–376.
Kendall, M.G., Moran, P.A.P. (1963). Geometrical Probability. Griffin, London.
Kingman, J.F.C. (1969). Random secants of a convex body. Journal of Applied Probability, 6, 660–672.
Miles, R.E. (1969). Poisson flats in Euclidean spaces. Part I: Finite numbers of random uniform flats. Advances in Applied Probability, 1, 211–237.
Moran, P.A.P. (1966). A note on recent research in geometrical probability. Journal of Applied Probability, 3, 453–463.
Moran, P.A.P. (1969). A second note on recent research in geometrical probability. Advances in Applied Probability, 1, 73–89.
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© 1981 D. Reidel Publishing Company
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Enns, E.G., Ehlers, P.F., Stuhr, S. (1981). Every Body has its Moments. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8552-0_30
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DOI: https://doi.org/10.1007/978-94-009-8552-0_30
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