On unfair permutations
| Autor: | İlker Arslan, Cihan Pehlivan, Ümit Işlak |
|---|---|
| Přispěvatelé: | Işık Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Işık University, Faculty of Arts and Sciences, Department of Mathematics, Arslan, İlker |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Class (set theory) Size biased coupling Central limit theorem Inverse 0102 computer and information sciences 01 natural sciences Combinatorics 010104 statistics & probability Descents Dependent random variables FOS: Mathematics Independent random 0101 mathematics Scaling Statistic Mathematics Random permutations Probability (math.PR) Stein's method Inversions 60C05 05A05 05A16 010201 computation theory & mathematics Uniform permutations Statistics Probability and Uncertainty Mathematics - Probability |
| Zdroj: | Statistics & Probability Letters. 141:31-40 |
| ISSN: | 0167-7152 |
| Popis: | In this paper we study the inverse of so-called unfair permutations, and explore various properties of them. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave very much alike for locally dependent random variables. As an example of a globally dependent statistic we use the number of inversions, and show that this statistic satisfies a central limit theorem after proper centering and scaling. A secondary example of a globally dependent statistic to be studied will be the number of fixed points. Finally, we introduce two different generalizations of inverse-unfair permutations. Final version after a major revision. An error in Proof of Theorem 4.1 is fixed |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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