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For a probability distribution $(p_s, s \in S)$ on a finite set $S$, call a random forest $F$ of rooted trees labeled by $S$ (with edges directed away from the roots) a (\em $p$-forest) if given $F$ has $m$ edges the vector of out-degrees of vertices of $F$ has a multinomial distribution with parameters $m$ and $(p_s,s \in S)$, and given also these out-degrees the distribution of $F$ is uniform on all forests with the given out-degrees. The family of distributions of $p$-forests is studied, and shown to be closed under various operations involving deletion of edges. Some related enumerations of rooted labeled forests are obtained as corollaries.

Details

Title
The multinomial distribution on rooted labeled forests
Creator
Pitman, Jim, Author
Published
Statistics Department, University of California, Berkeley, University of California at Berkeley, Berkeley, California, Jun 1998
Full Collection Name
Statistics Technical Reports
Other Identifiers
499
Type
Text
Format
technical reports
Archive
Mathematics Statistics Library
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