On leaf related statistics in recursive tree models
Statistics and Probability Letters, cilt.121, ss.61-69, 2017 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 121
- Basım Tarihi: 2017
- Doi Numarası: 10.1016/j.spl.2016.10.007
- Dergi Adı: Statistics and Probability Letters
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.61-69
- Anahtar Kelimeler: Central limit theorem, Number of leaves, Riffle-shuffle distribution, Stein's method, Uniform recursive tree
- Boğaziçi Üniversitesi Adresli: Evet
Özet
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.