Nous y introduisons une nouvelle classe de distributions bivariées de type Marshall-Olkin, la distribution Erlang bivariée. La transformée de Laplace, les moments et les densités conditionnelles y sont obtenus. Les applications potentielles en assurance-vie et en finance sont prises en considération. Les estimateurs du maximum de vraisemblance des paramètres sont calculés par l'algorithme Espérance-Maximisation. Ensuite, notre projet de recherche est consacré à l'étude des processus de risque multivariés, qui peuvent être utiles dans l'étude des problèmes de la ruine des compagnies d'assurance avec des classes dépendantes. Nous appliquons les résultats de la théorie des processus de Markov déterministes par morceaux afin d'obtenir les martingales exponentielles, nécessaires pour établir des bornes supérieures calculables pour la probabilité de ruine, dont les expressions sont intraitables. / In this contribution, we introduce a new class of bivariate distributions of Marshall-Olkin type, called bivariate Erlang distributions. The Laplace transform, product moments and conditional densities are derived. Potential applications of bivariate Erlang distributions in life insurance and finance are considered. Further, our research project is devoted to the study of multivariate risk processes, which may be useful in analyzing ruin problems for insurance companies with a portfolio of dependent classes of business. We apply results from the theory of piecewise deterministic Markov processes in order to derive exponential martingales needed to establish computable upper bounds of the ruin probabilities, as their exact expressions are intractable.

This thesis is related to the Bit Error Rate (BER) estimation for any digital communication system. In many designs of communication systems, the BER is a Key Performance Indicator (KPI). The popular Monte-Carlo (MC) simulation technique is well suited to any system but at the expense of long time simulations when dealing with very low error rates. In this thesis, we propose to estimate the BER by using the Probability Density Function (PDF) estimation of the soft observations of the received bits. First, we have studied a non-parametric PDF estimation technique named the Kernel method. Simulation results in the context of several digital communication systems are proposed. Compared with the conventional MC method, the proposed Kernel-based estimator provides good precision even for high SNR with very limited number of data samples. Second, the Gaussian Mixture Model (GMM), which is a semi-parametric PDF estimation technique, is used to estimate the BER. Compared with the Kernel-based estimator, the GMM method provides better performance in the sense of minimum variance of the estimator. Finally, we have investigated the blind estimation of the BER, which is the estimation when the sent data are unknown. We denote this case as unsupervised BER estimation. The Stochastic Expectation-Maximization (SEM) algorithm combined with the Kernel or GMM PDF estimation methods has been used to solve this issue. By analyzing the simulation results, we show that the obtained BER estimate can be very close to the real values. This is quite promising since it could enable real-time BER estimation on the receiver side without decreasing the user bit rate with pilot symbols for example.

Introduction: No Fixed-Dose Combination (FDC) formulations currently exist for pediatric tuberculosis (TB) treatment. Earlier work implemented, in the software NONMEM, a rational method for optimizing design and individualization of pediatric anti-TB FDC formulations based on patient body weight, but issues with parameter estimation, dosage strata heterogeneity and representative pharmacokinetics remained. Aim: To further develop the rational model-based methodology aiding the selection of appropriate FDC formulation designs and dosage regimens, in pediatric TB treatment. Materials and Methods: Optimization of the method with respect to the estimation of body weight breakpoints was sought. Heterogeneity of dosage groups with respect to treatment efficiency was sought to be improved. Recently published pediatric pharmacokinetic parameters were implemented and the model translated to MATLAB, where also the performance was evaluated by stochastic estimation and graphical visualization. Results: A logistic function was found better suited as an approximation of breakpoints. None of the estimation methods implemented in NONMEM were more suitable than the originally used FO method. Homogenization of dosage group treatment efficiency could not be solved. MATLAB translation was successful but required stochastic estimations and highlighted high densities of local minima. Representative pharmacokinetics were successfully implemented. Conclusions: NONMEM was found suboptimal for the task due to problems with discontinuities and heterogeneity, but a stepwise method with representative pharmacokinetics were successfully implemented. MATLAB showed more promise in the search for a method also addressing the heterogeneity issue.

Les dispositifs de protection de sites sensibles doivent permettre de détecter des menaces potentielles suffisamment à l’avance pour pouvoir mettre en place une stratégie de défense. Dans cette optique, les méthodes de détection et de reconnaissance d’aéronefs se basant sur des images infrarouge multispectrales doivent être adaptées à des images faiblement résolues et être robustes à la variabilité spectrale et spatiale des cibles. Nous mettons au point dans cette thèse, des méthodes statistiques de détection et de reconnaissance d’aéronefs satisfaisant ces contraintes. Tout d’abord, nous spécifions une méthode de détection d’anomalies pour des images multispectrales, combinant un calcul de vraisemblance spectrale avec une étude sur les ensembles de niveaux de la transformée de Mahalanobis de l’image. Cette méthode ne nécessite aucune information a priori sur les aéronefs et nous permet d’identifier les images contenant des cibles. Ces images sont ensuite considérées comme des réalisations d’un modèle statistique d’observations fluctuant spectralement et spatialement autour de formes caractéristiques inconnues. L’estimation des paramètres de ce modèle est réalisée par une nouvelle méthodologie d’apprentissage séquentiel non supervisé pour des modèles à données manquantes que nous avons développée. La mise au point de ce modèle nous permet in fine de proposer une méthode de reconnaissance de cibles basée sur l’estimateur du maximum de vraisemblance a posteriori. Les résultats encourageants, tant en détection qu’en classification, justifient l’intérêt du développement de dispositifs permettant l’acquisition d’images multispectrales. Ces méthodes nous ont également permis d’identifier les regroupements de bandes spectrales optimales pour la détection et la reconnaissance d’aéronefs faiblement résolus en infrarouge / Surveillance systems should be able to detect potential threats far ahead in order to put forward a defence strategy. In this context, detection and recognition methods making use of multispectral infrared images should cope with low resolution signals and handle both spectral and spatial variability of the targets. We introduce in this PhD thesis a novel statistical methodology to perform aircraft detection and classification which take into account these constraints. We first propose an anomaly detection method designed for multispectral images, which combines a spectral likelihood measure and a level set study of the image Mahalanobis transform. This technique allows to identify images which feature an anomaly without any prior knowledge on the target. In a second time, these images are used as realizations of a statistical model in which the observations are described as random spectral and spatial deformation of prototype shapes. The model inference, and in particular the prototype shape estimation, is achieved through a novel unsupervised sequential learning algorithm designed for missing data models. This model allows to propose a classification algorithm based on maximum a posteriori probability Promising results in detection as well as in classification, justify the growing interest surrounding the development of multispectral imaging devices. These methods have also allowed us to identify the optimal infrared spectral band regroupments regarding the low resolution aircraft IRS detection and classification

本研究利用美國芝加哥商品交易所針對 18 個城市發行之冷氣指數／暖氣指數衍生性商品與相對應之日均溫進行分析與評價。研究成果與貢獻如下：一、延伸 Alaton, Djehince, and Stillberg (2002) 模型，引入跳躍風險、隨機波動度、波動跳躍等因子，提出新模型以捕捉更多溫度指數之特徵。二、針對不同模型，分別利用最大概似法、期望最大演算法、粒子濾波演算法等進行參數估計。實證結果顯示新模型具有較好之配適能力。三、利用 Esscher 轉換將真實機率測度轉換至風險中立機率測度，並進一步利用　Feynman-Kac 方程式與傅立葉轉換求出溫度模型之機率分配。四、推導冷氣指數／暖氣指數期貨之半封閉評價公式，而冷氣指數／暖氣指數期貨之選擇權不存在封閉評價公式，則利用蒙地卡羅模擬進行評價。五、無論樣本內與樣本外之定價誤差，考慮隨機波動度型態之模型對於溫度衍生性商品皆具有較好之評價績效。六、實證指出溫度市場之市場風險價格為負，顯示投資人承受較高之溫度風險時會要求較高之風險溢酬。本研究可給予受溫度風險影響之產業，針對衍生性商品之評價與模型參數估計上提供較為精準、客觀與較有效率之工具。 / This study uses the daily average temperature index (DAT) and market price of the CDD/HDD derivatives for 18 cities from the CME group. There are some contributions in this study: (i) we extend the Alaton, Djehince, and Stillberg (2002)'s framework by introducing the jump risk, the stochastic volatility, and the jump in volatility. (ii) The model parameters are estimated by the MLE, the EM algorithm, and the PF algorithm. And, the complex model exists the better goodness-of-fit for the path of the temperature index. (iii) We employ the Esscher transform to change the probability measure and derive the probability density function of each model by the Feynman-Kac formula and the Fourier transform. (iv) The semi-closed form of the CDD/HDD futures pricing formula is derived, and we use the Monte-Carlo simulation to value the CDD/HDD futures options due to no closed-form solution. (v) Whatever in-sample and out-of-sample pricing performance, the type of the stochastic volatility performs the better fitting for the temperature derivatives. (vi) The market price of risk differs to zero significantly (most are negative), so the investors require the positive weather risk premium for the derivatives. The results in this study can provide the guide of fitting model and pricing derivatives to the weather-linked institutions in the future.