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Exact Distributional Results for Random Resistance Trees
Author(s) -
BarndorffNielsen Ole E.,
Rydberg Tina Hviid
Publication year - 2000
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00183
Subject(s) - mathematics , inverse gaussian distribution , reciprocal , inverse distribution , inverse gamma distribution , gaussian , statistic , inverse , convolution (computer science) , conditional probability distribution , statistics , gamma distribution , tree (set theory) , distribution (mathematics) , statistical physics , combinatorics , probability distribution , mathematical analysis , heavy tailed distribution , geometry , inverse chi squared distribution , distribution fitting , philosophy , linguistics , physics , quantum mechanics , machine learning , artificial neural network , computer science
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.