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Limit Distributions and Random Trees Derived from the Birthday Problem with Unequal Probabilities


 
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1. Title Title of document Limit Distributions and Random Trees Derived from the Birthday Problem with Unequal Probabilities
 
2. Creator Author's name, affiliation, country Michael Camarri; University of California, Berkeley
 
2. Creator Author's name, affiliation, country Jim Pitman; University of California, Berkeley
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Repeat times, point process, Poisson embedding, inhomogeneous continuum random tree, Rayleigh distribution
 
3. Subject Subject classification 60G55, 05C05
 
4. Description Abstract Given an arbitrary distribution on a countable set, consider the number of independent samples required until the first repeated value is seen. Exact and asymptotic formulae are derived for the distribution of this time and of the times until subsequent repeats. Asymptotic properties of the repeat times are derived by embedding in a Poisson process. In particular, necessary and sufficient conditions for convergence are given and the possible limits explicitly described. Under the same conditions the finite dimensional distributions of the repeat times converge to the arrival times of suitably modified Poisson processes, and random trees derived from the sequence of independent trials converge in distribution to an inhomogeneous continuum random tree.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1999-11-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/58
 
10. Identifier Digital Object Identifier 10.1214/EJP.v5-58
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 5
 
12. Language English=en
 
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