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On the volume distribution of the typical Poisson–Delaunay cell

Part of: Stochastic processes Discrete geometry

Published online by Cambridge University Press:  14 July 2016

P. N. Rathie
P. N. Rathie*
Affiliation:
State University of Campinas
*
∗Postal address: Departamento de Estatistica-ICEX, Universidade Estadual de Minas Gerais, Caixa Postal 702, Cidade Universitaria-Pampulha 31270 Belo Horizonte, MG, Brazil.
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Abstract

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A method of obtaining the distribution of the volume of the typical cell of a Delaunay tessellation generated by a Poisson process in is developed and used to derive the density when d = 1, 2, 3.

Keywords

DELAUNAY TESSELLATIONEXACT VOLUME DISTRIBUTION

MSC classification

Primary: 52C17: Packing and covering in $n$ dimensions
Secondary: 60G55: Point processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 3 , September 1992 , pp. 740 - 744
Copyright
Copyright © Applied Probability Trust 1992 

Footnotes

This work was completed while the author was visiting McGill University, Montreal, Canada and the University of Rajasthan, Jaipur, India during 1990. Supported, partially, by FAPESP Grant No. 89/2199-8.

References

Erdélyi, A. et al. (1953) Higher Transcendental Functions, Vol. I. McGraw-Hill, New York.Google Scholar
Erdélyi, A. et al. (1954) Tables of Integral Transforms, Vol. II. McGraw-Hill, New York.Google Scholar
Luke, Y. L. (1969) The Special Functions and their Approximations, Vol. I. Academic Press, New York.Google Scholar
Mathai, A. M. and Rathie, P. N. (1971) The exact distribution of Wilks' criterion. Ann. Math. Statist. 42, 1010–1019.Google Scholar
Miles, R. E. (1972) The random division of space. Suppl. Adv. Appl. Prob. 243–266.CrossRefGoogle Scholar
Miles, R. E. (1974) A synopsis of ‘Poisson flats in Euclidean spaces’. In Stochastic Geometry, ed. Harding, E. F. and Kendall, D. G., Wiley, New York.Google Scholar
Møller, J. (1989) Random tessellations in. Adv. Appl. Prob. 21, 37–73.Google Scholar
Rao, C. R. (1965) Linear Statistical Inference and its Applications. Wiley, New York.Google Scholar
Rathie, P. N. (1989) Generalized hypergeometric functions and exact distributions of test statistics. Amer. J. Math. Manag. Sci. 9, 155–172.Google Scholar
Rogers, C. A. (1964) Packing and Covering. Cambridge University Press, London.Google Scholar