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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1998-19
September 1998

Exact Distributional Results for Random Resistance Trees


Ole E. Barndorff-Nielsen

Tina Hviid Rydberg


With a view to the study of, for instance, arterial trees, this paper presents some exact distributional results on finite trees with (reciprocal) inverse Gaussian and gamma resistances. In particular, it is shown that under the specified model the conditional distribution of the minimal sufficient statistic given the total resistance of the tree is a convolution of gamma distributions and two-dimensional reciprocal inverse Gaussian distributions.

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This paper has now been published in Scand. J. Statist. 27 (2000), no. 1, 129--141