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    The variance of the average depth of a pure birth process converges to 7

    Duffy, Ken R. and 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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    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:
    Depositing User: Dr Ken Duffy
    Date Deposited: 02 Nov 2020 16:19
    Journal or Publication Title: Statistics and Probability Letters
    Publisher: Elsevier
    Refereed: Yes
    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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