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A Note on Electrical Networks and the Inverse Gaussian Distribution

Part of: Geometric probability and stochastic geometry Distribution theory Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  01 July 2016

O. E. Barndorff-Nielsen
O. E. Barndorff-Nielsen*
Affiliation:
Aarhus University
*
* Postal address: Department of Theoretical Statistics, Institute of Mathematics, Ny Munkegade, DK-8000 Aarhus C, Denmark.
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Abstract

When a random electrical network has the structure of a rooted tree and the edge resistances are either inverse Gaussian or reciprocal inverse Gaussian random variables then, subject to some restrictions, the overall resistance of the network is shown to follow a reciprocal inverse Gaussian distribution.

Keywords

RANDOM GRAPHROOTED TREEKIRCHHOFF'S LAWS

MSC classification

Primary: 60B99: None of the above, but in this section
Secondary: 60D05: Geometric probability and stochastic geometry 62E99: None of the above, but in this section
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 63 - 67
Copyright
Copyright © Applied Probability Trust 1994 

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References

Barndorff-Nielsen, O. E. and BlæSild, P. (1988) Combination of reproductive models. Ann. Statist. 16, 323–341.CrossRefGoogle Scholar
Chartrand, G. and Lesniak, L. (1986) Graphs and Digraphs. Wadsworth and Brooks/Cole, Monterey, CA.Google Scholar
Grimmett, G. (1993) Random graphical networks. In Chaos and Networks. Statistical and Probabilistic Aspects, ed. Barndorff-Nielsen, O. E., Jensen, J. L. and Kendall, W. S., pp. 288–301, Chapman and Hall, London.Google Scholar
Kesten, H. (1982) Percolation Theory for Mathematicians. Birkhäuser, Basel.CrossRefGoogle Scholar