| Titre : | Trimmed L-moment, estimators and application |
| Auteurs : | Sara Gherraf, Auteur ; Fatah Benatia, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2025 |
| Format : | 1 vol. (48 p.) |
| Langues: | Anglais |
| Résumé : |
In this work, which focuses on estimation methods of L-moments and trimmed L-moments, we recalled the definitions and characteristics related to random vectors and order statistics that are necessary for understanding the content. Then, we presented the method for estimating L-moments by outlining its definition, properties, and statistical advantages. We also addressed the trimmed L-moments by highlighting their robustness and consistency, which surpass those of the classical method of moments thanks to the elimination of extreme and outlier values. Finally, an application based on simulation was carried out to estimate the parameters of different distributions using estimators of L-parameters such as L-skewness and L-kurtosis... In this work, which focuses on estimation methods of L-moments and trimmed L-moments, we recalled the definitions and characteristics related to random vectors and order statistics that are necessary for understanding the content. Then, we presented the method for estimating L-moments by outlining its definition, properties, and statistical advantages. We also addressed the trimmed L-moments by highlighting their robustness and consistency, which surpass those of the classical method of moments thanks to the elimination of extreme and outlier values. Finally, an application based on simulation was carried out to estimate the parameters of different distributions using estimators of L-parameters such as L-skewness and L-kurtosis... |
| Sommaire : |
Dedication I Acknowledgment I List of tables VI Introduction 1 1 Random vector and Order Statistics 3 1.1 Random variable and Random vector . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Probability space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Random variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Probability distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.4 The moment of a random variable . . . . . . . . . . . . . . . . . . . . . . 4 1.1.5 Random vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.6 Moment of random vector . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.7 Covariance matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.8 Independence and identically distributed of two variables . . . . . . . . 10 1.1.9 Characteristic Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Order statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.1 law of the i-th order statistics . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Moment of order statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 L-moments 15 2.1 Definitions and basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 L-parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 L-moment using polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.1 Example (Weibull distribution) . . . . . . . . . . . . . . . . . . . . . . . 19 IV2.4 L-moment using covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Example(Uniform distribution) . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 L-moment in terms of probability weighted moments . . . . . . . . . . . . . . . 22 2.5.1 Example(exponential distribution) . . . . . . . . . . . . . . . . . . . . . . 23 2.5.2 Examples(usuels distribution) . . . . . . . . . . . . . . . . . . . . . . . . 25 2.6 L-moment λk by Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.7 Estimation of L-moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.8 Estimation of parameters by L-moment . . . . . . . . . . . . . . . . . . . . . . 28 2.8.1 Example(Weibull distribution) . . . . . . . . . . . . . . . . . . . . . . . . 29 2.8.2 L-moment Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Trimmed L-moment 33 3.1 Definitions and basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 TL-parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3 proprieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4 Estimation of trimmed L-moments . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.5 application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.5.1 Exemple(cauchy) . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 41 3.6 application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.6.1 Exemple(generalized pareto) . . . . . . . . . . . . . . . . . . . . . . . . . 44 Conclusion 48 Bibliography i V |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| MM/1333 | Mémoire master | bibliothèque sciences exactes | Consultable |
