| Titre : | Modeling of rare events for risk management |
| Auteurs : | Sana Benameur, Auteur ; Djamel Meraghni, 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, 2018 |
| Format : | 1 vol. (117 p.) / 30 cm |
| Langues: | Anglais |
| Mots-clés: | Extreme values ; Flood discharges ; Frequency analysis ; General- ized Pareto distribution ; Heavy-tailed distributions ; High quantiles ; Rare events ; Return levels ; Risk measures ; Tail index. |
| Résumé : | Nowadays, risk management plays a key role especially in socio-economic world such as: commerce, industry, agriculture, finance, insurance, soci- ology, medicine, politics and sport, etc. Hence we need some tools in order to control that risk. So we define theoretical quantities that we call risk measures and we will be able to estimate it appropriately. It is obvious that in order to make a precise estimate, we must find the theoretical model most appropriate to the data. This is done using extreme value theory, which seems to be the best tool for modeling rare events that greatly influence the behavior of companies to deal with dangerous risks. This study aims to estimate the various parameters of a model of extreme values in order to be able to approach the estimation of the risk measures. Those results will be applied especially in extreme hydrological events such as floods, which are one of the natural disasters that occur in several parts of the world. They are regarded as being the most costly natural risks in terms of the disastrous consequences in human lives and in property damages. The main objective of the present study is to estimate flood events of Abiod wadi at given return periods at the gauge station of M'chouneche, located closely to the city of Biskra in a semiarid region of southern east of Algeria. This is a problematic issue in several ways, because of the existence of a dam to the downstream, including the field of the sedimentation and the water leaks through the dam during floods. A complete frequency analysis is performed on a series of observed daily aver- age discharges, including classical statistical tools as well as recent techniques. The obtained results show that the generalized Pareto distribution (GPD), for which the parameters were estimated by the maximum likelihood (ML) method, describes the analyzed series better. This study also indicates to the decision- makers the importance to continue |
| Sommaire : |
Achieved Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 I Preliminary Theory 5 Chapter 1. Extreme Values . . . . . . . . . . . . . . . . . . . . . . 6 1.1. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1. Law of Large Numbers . . . . . . . . . . . . . . . . . . . . 7 1.1.2. Central Limit Theorem . . . . . . . . . . . . . . . . . . . . 9 1.2. Order Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1. Distribution of An Order Statistics . . . . . . . . . . . . . 9 1.2.2. Joint Density of Two Order Statistics . . . . . . . . . . . . 11 1.2.3. Joint Density of All the Order Statistics . . . . . . . . . . 11 1.2.4. Some Properties of Order Statistics . . . . . . . . . . . . . 12 1.2.5. Properties of Uniform and Exponential Spacings . . . . . . 13 1.3. Limit Distributions and Domains of Attraction . . . . . . . . . . . 14 1.3.1. Regular Variation . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2. GEV Approximation . . . . . . . . . . . . . . . . . . . . . 19 Contents— Continued vii 1.3.3. Maximum Domains of Attraction . . . . . . . . . . . . . . 21 1.3.4. GPD Approximation . . . . . . . . . . . . . . . . . . . . . 25 Chapter 2. Estimation of Tail Index, High Quantiles and Risk Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1. Parameters Estimation Procedures of the GEV Distribution . . . 32 2.1.1. Parametric Approach . . . . . . . . . . . . . . . . . . . . . 33 2.1.2. Semi-Parametric Approach . . . . . . . . . . . . . . . . . . 36 2.2. POT Model Estimation Procedure . . . . . . . . . . . . . . . . . 53 2.2.1. Maximum Likelihood Method (ML) . . . . . . . . . . . . . 54 2.2.2. Probability Weighted Moment Method (PWM) . . . . . . 55 2.2.3. Estimating Distribution Tails . . . . . . . . . . . . . . . . 55 2.3. Optimal Sample Fraction Selection . . . . . . . . . . . . . . . . . 56 2.3.1. Graphical Method . . . . . . . . . . . . . . . . . . . . . . 56 2.3.2. Minimization of the Asymptotic Mean Square Error . . . . 56 2.3.3. Adaptive Procedures . . . . . . . . . . . . . . . . . . . . . 57 2.3.4. Threshold Selection . . . . . . . . . . . . . . . . . . . . . . 61 2.4. Estimating High Quantiles . . . . . . . . . . . . . . . . . . . . . . 62 2.4.1. GEV Distribution Based Estimators . . . . . . . . . . . . 63 2.4.2. Estimators Based on the POT Models . . . . . . . . . . . 65 2.5. Risk Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.5.1. De…nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.5.2. Premium Calculation Principles . . . . . . . . . . . . . . . 68 2.5.3. Some premium principles . . . . . . . . . . . . . . . . . . . 73 2.5.4. Risk Measures . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.5.5. Relationships Between Risk Measures . . . . . . . . . . . . 79 2.5.6. Estimating Risk Measures . . . . . . . . . . . . . . . . . . 80 II Main Results 82 Chapter 3. Complete Flood Frequency Analysis in Abiod Wa- tershed Biskra (Algeria) . . . . . . . . . . . . . . . . . . . . . . . 83 3.1. Study Area and Data . . . . . . . . . . . . . . . . . . . . . . . . . 84 Table of Contents viii 3.1.1. Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.1.2. Data Description . . . . . . . . . . . . . . . . . . . . . . . 86 3.2. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.2.1. Peaks Over Threshold Series . . . . . . . . . . . . . . . . . 87 3.2.2. Exploratory Data Analysis . . . . . . . . . . . . . . . . . . 89 3.2.3. Testing Independence, Stationarity and Homogeneity . . . 89 3.2.4. Parameter Estimation and Model Selection . . . . . . . . . 90 3.2.5. Quantile Estimation . . . . . . . . . . . . . . . . . . . . . 91 3.3. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 92 3.3.1. Exploratory Analysis and Outlier Detection . . . . . . . . 92 3.3.2. Testing the Basic FA Assumptions . . . . . . . . . . . . . 97 3.3.3. Model Fitting . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.3.4. Quantile Estimation . . . . . . . . . . . . . . . . . . . . . 98 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Abbreviations and Notations . . . . . . . . . . . . . . . . . . . . . . 103 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 |
| En ligne : | http://thesis.univ-biskra.dz/3668/1/Th%C3%A8se%20de%20doctorat%20Benameur%20Sana.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/80 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
