| Titre : | L-Statistics and applications |
| Auteurs : | Lamia Hamidat, Auteur ; Abdelhakim Necir , Directeur de thèse |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2024 |
| Format : | 1 vol. (106 p.) / couv. ill. en coul / 30cm |
| Langues: | Anglais |
| Résumé : |
L-statistics offer significant advantages in statistic analysis due to its robustness, simplicity, and wide applicability. Their ability to summarize data using linear combinations of order statistics makes them particularly resistant to outliers and nonnormal data distributions. This robustness is essential for producing reliable results in real-world scenarios where data often deviate from ideal conditions. The simplicity of L-statistics lies in their straightforward computational nature. Unlike more complex methods that require intricate algorithms and intensive calculations. |
| Sommaire : |
Acknowledgements ii Contents iii Tables list 0-5 1 Order statistics 1-9 1.1 Order statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9 1.2 Distribution functions of order statistics . . . . . . . . . . . . . . . . 1-10 1.2.1 Distribution functions of smallest and largest order statistics . 1-10 1.2.2 Distribution function of the i-th order statistic . . . . . . . . . 1-11 1.3 Basic distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11 1.3.1 Joint distribution function of n order statistics . . . . . . . . . 1-11 1.3.2 Joint distribution function of a couple order statistics . . . . . 1-12 1.4 Moments of order statistics . . . . . . . . . . . . . . . . . . . . . . . . 1-12 2 L-Statistics and applications 2-17 2.1 Application of L-statistics . . . . . . . . . . . . . . . . . . . . . . . . 2-19 3 Linear estimators of order statistics 3-23 3.1 L-moment estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23 3.1.1 L-functional representation of L-moments . . . . . . . . . . . . 3-24 3.1.2 L-moments based estimation . . . . . . . . . . . . . . . . . . . 3-25 3.2 Asymptotic e¢ cient estimators . . . . . . . . . . . . . . . . . . . . . 3-33 3.3 Best linear unbiased estimators . . . . . . . . . . . . . . . . . . . . . 3-47 4 Simulation study and real data applications 4-50 4.1 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-50 4.1.1 The most packages used in our simulation . . . . . . . . . . . 4-51 4.2 Real data applications . . . . . . . . . . . . . . . . . . . . . . . . . . 4-54 4.2.1 The packages used in our real data program . . . . . . . . . . 4-55 5 Appendix 5-60 5.1 Appendix A: R Software . . . . . . . . . . . . . . . . . . . . . . . . . 5-60 5.1.1 What is the R language? . . . . . . . . . . . . . . . . . . . . . 5-60 5.2 Appendix B: Abbreviations and Notations . . . . . . . . . . . . . . . 5-61 5.3 Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-61 5.3.1 Asymptotic proprities . . . . . . . . . . . . . . . . . . . . . . 5-61 5.3.2 Simulation codes . . . . . . . . . . . . . . . . . . . . . . . . . 5-62 5.3.3 Real data codes . . . . . . . . . . . . . . . . . . . . . . . . . . 5-106 |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| MM/1277 | Mémoire master | bibliothèque sciences exactes | Consultable |
