Random Discrete Distributions Derived from Self-Similar Random Sets
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | Random Discrete Distributions Derived from Self-Similar Random Sets |
| 2. | Creator | Author's name, affiliation, country | Jim Pitman; University of California, Berkeley |
| 2. | Creator | Author's name, affiliation, country | Marc Yor; Université Pierre et Marie Curie |
| 3. | Subject | Discipline(s) | Mathematics |
| 3. | Subject | Keyword(s) | interval partition, zero set, excursion lengths, regenerative set, structural distribution. |
| 3. | Subject | Subject classification | 60G18, 60G57, 60K05. |
| 4. | Description | Abstract | A model is proposed for a decreasing sequence of random variables $(V_1, V_2, \cdots)$ with $\sum_n V_n = 1$, which generalizes the Poisson-Dirichlet distribution and the distribution of ranked lengths of excursions of a Brownian motion or recurrent Bessel process. Let $V_n$ be the length of the $n$th longest component interval of $[0,1]\backslash Z$, where $Z$ is an a.s. non-empty random closed of $(0,\infty)$ of Lebesgue measure $0$, and $Z$ is self-similar, i.e. $cZ$ has the same distribution as $Z$ for every $c > 0$. Then for $0 \le a < b \le 1$ the expected number of $n$'s such that $V_n \in (a,b)$ equals $\int_a^b v^{-1} F(dv)$ where the structural distribution $F$ is identical to the distribution of $1 - \sup ( Z \cap [0,1] )$. Then $F(dv) = f(v)dv$ where $(1-v) f(v)$ is a decreasing function of $v$, and every such probability distribution $F$ on $[0,1]$ can arise from this construction. |
| 5. | Publisher | Organizing agency, location | |
| 6. | Contributor | Sponsor(s) | |
| 7. | Date | (YYYY-MM-DD) | 1996-02-20 |
| 8. | Type | Status & genre | Peer-reviewed Article |
| 8. | Type | Type | |
| 9. | Format | File format | |
| 10. | Identifier | Uniform Resource Identifier | http://ejp.ejpecp.org/article/view/4 |
| 10. | Identifier | Digital Object Identifier | 10.1214/EJP.v1-4 |
| 11. | Source | Journal/conference title; vol., no. (year) | Electronic Journal of Probability; Vol 1 |
| 12. | Language | English=en | en |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
| 15. | Rights | Copyright and permissions | The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free
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