On leaf related statistics in recursive tree models
| Autor: | Serdar Altok, Ümit Işlak |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Discrete mathematics 010102 general mathematics Asymptotic distribution Stein's method Recursive partitioning Random permutation 01 natural sciences Recursive tree Combinatorics 010104 statistics & probability Simple (abstract algebra) Statistics Bijection 0101 mathematics Statistics Probability and Uncertainty Central limit theorem Mathematics |
| Zdroj: | Statistics & Probability Letters. 121:61-69 |
| ISSN: | 0167-7152 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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