MPS-RR 1998-19
September 1998

Exact Distributional Results for Random Resistance Trees

Ole E. Barndorff-Nielsen

Tina Hviid Rydberg

Abstract

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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