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Duffy, Ken R., Meli, Gianfelice and Shneer, Seva (2019) The variance of the average depth of a pure birth process converges to 7. Statistics and Probability Letters, 150. pp. 88-93. ISSN 0167-7152
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Abstract
If trees are constructed from a pure birth process and one defines the depth of a leaf
to be the number of edges to its root, it is known that the variance in the depth of a
randomly selected leaf of a randomly selected tree grows linearly in time. In this letter,
we instead consider the variance of the average depth of leaves within each individual
tree, establishing that, in contrast, it converges to a constant, 7. This result indicates
that while the variance in leaf depths amongst the ensemble of pure birth processes
undergoes large fluctuations, the average depth across individual trees is much more
consistent.
| Item Type: | Article |
|---|---|
| Keywords: | Pure birth process; Variance of the average depth; |
| Academic Unit: | Faculty of Science and Engineering > Research Institutes > Hamilton Institute |
| Item ID: | 13475 |
| Identification Number: | 10.1016/j.spl.2019.02.015 |
| Depositing User: | Dr Ken Duffy |
| Date Deposited: | 02 Nov 2020 16:19 |
| Journal or Publication Title: | Statistics and Probability Letters |
| Publisher: | Elsevier |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mu.eprints-hosting.org/id/eprint/13475 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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