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On leaf related statistics in recursive tree models

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  • Altok, S.
  • Işlak, Ü.

Abstract

Using a bijection between a uniformly random permutation and a uniform recursive tree (URT), we give a simple proof of a recent result of Zhang that shows the asymptotic normality of the number of leaves in a URT with convergence rates. We also show that a similar result holds for a more general class of statistics related to URTs, that we call the number of runs of leaves in a URT. The second, and the main, purpose of the current note is to introduce and to study a non-uniform recursive tree model by exploiting the bijection between permutations and recursive trees. This may provide a useful framework for constructing various types of random trees.

Suggested Citation

  • Altok, S. & Işlak, Ü., 2017. "On leaf related statistics in recursive tree models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 61-69.
    • Handle: RePEc:eee:stapro:v:121:y:2017:i:c:p:61-69
    DOI: 10.1016/j.spl.2016.10.007
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    References listed on IDEAS

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    1. J. L. Gastwirth & P. K. Bhattacharya, 1984. "Two Probability Models of Pyramid or Chain Letter Schemes Demonstrating that Their Promotional Claims are Unreliable," Operations Research, INFORMS, vol. 32(3), pages 527-536, June.
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