Made available in DSpace on 2016-06-02T20:06:06Z (GMT). No. of bitstreams: 1 4331.pdf: 1908865 bytes, checksum: d564b46a6111fdca6f7cc9f4d5596637 (MD5) Previous issue date: 2009-03-18 / Universidade Federal de Minas Gerais / The Weibull distribuition is a common initial choice for modeling data with monotone hazard rates. However, such distribution fails to provide a reasonable parametric _t when the hazard function is unimodal or bathtub-shaped. In this context, Cooray (2006) proposed a generalization of the Weibull family by considering the distributions of the odds of Weibull and inverse Weibull families, referred as the odd Weibull family which is not just useful for modeling unimodal and bathtub-shaped hazards, but it is also convenient for testing goodness-of-_t of Weibull and inverse Weibull as submodels. In this project we have systematically studied the odd Weibull family along with its properties, showing motivations for its utilization, inserting covariates in the model, pointing out some troubles associated with the maximum likelihood estimation and proposing interval estimation and hypothesis test construction methodologies for the model parameters. We have also compared resampling results with asymptotic ones. Coverage probability from proposed con_dence intervals and size and power of considered hypothesis tests were both analyzed as well via Monte Carlo simulation. Furthermore, we have proposed a Bayesian estimation methodology for the model parameters based in Monte Carlo Markov Chain (MCMC) simulation techniques. / A distribuição Weibull é uma escolha inicial freqüente para modelagem de dados com taxas de risco monótonas. Entretanto, esta distribuição não fornece um ajuste paramétrico razoável quando as funções de risco assumem um formato unimodal ou em forma de banheira. Neste contexto, Cooray (2006) propôs uma generalização da família Weibull considerando a distribuição da razão de chances das famílias Weibull e Weibull inversa, referida como família Weibull de razão de chances. Esta família não é apenas conveniente para modelar taxas de risco unimodal e banheira, mas também é adequada para testar a adequabilidade do ajuste das famílias Weibull e Weibull inversa como submodelos. Neste trabalho, estudamos sistematicamente a família Weibull de razão de chances e suas propriedades, apontando as motivações para o seu uso, inserindo covariáveis no modelo, veri_cando as di_culdades referentes ao problema da estimação de máxima verossimilhança dos parâmetros do modelo e propondo metodologia de estimação intervalar e construção de testes de hipóteses para os parâmetros do modelo. Comparamos os resultados obtidos por meio dos métodos de reamostragem com os resultados obtidos via teoria assintótica. Tanto a probabilidade de cobertura dos intervalos de con_ança propostos quanto o tamanho e poder dos testes de hipóteses considerados foram estudados via simulação de Monte Carlo. Além disso, propusemos uma metodologia Bayesiana de estimação para os parâmetros do modelo baseados em técnicas de simulação de Monte Carlo via Cadeias de Markov.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This paper has as its main purpose to highlight some mathematical concepts, which are behind the ranking given by a research made on the website mostly used in the world: Google. At the beginning, we briefly approached some High School’s concepts, such as: Matrices, Linear Systems and Probability. After that, we presented some basic notions related to Directed Graphs and Markov Chains of Discrete Time. From this last one, we gave more emphasis to the Steady State Vector because it ensures foreknowledge results from long-term. These concepts are extremely important to our paper, because they will be used to explain the involvement of Mathematic behind the web search “Google”. Then, we tried to detail the ranking operation of the search pages on Google, i.e., how the results of a research are classified, determining which results are presented in a sequential way in order of relevance. Finally we obtained “PageRank”, an algorithm which creates what we call Google’s Matrices and ranks the pages of a search. We finished making a brief comment about the historical arising of the web searches, from their founders to the rise and hegemony of Google. / O presente trabalho tem como objetivo destacar alguns conceitos matemáticos que estão por trás do ranqueamento dado por uma pesquisa feita no site de busca mais usados do mundo, o “Google”. Inicialmente abordamos de forma breve alguns conteúdos da matemática do ensino médio, a exemplo de: matrizes, sistemas lineares, probabilidades. Em seguida são introduzidas noções básicas de grafos dirigidos e cadeias de Markov de tempo discreto; essa última, é dada uma ênfase ao vetor estado estacionário, por ele garantir resultados de previsão de longo prazo. Esses conceitos são de grande importância em nosso trabalho, pois serão usados para explicar o envolvimento da matemática por trás do site de buscas “Google”. Na sequência, buscamos detalhar o funcionamento do ranqueamento das páginas de uma busca no “Google”, isto é, como são classificados os resultados de uma pesquisa, determinando quais resultados serão apresentados de modo sequencial em ordem de relevância. Finalmente, chegamos na obtenção do “PageRank”, algoritmo que gera a chamada Matriz do Google e ranqueia as páginas de uma busca. Encerramos com um breve histórico do surgimento dos sites de buscas, desde os seus fundadores até a ascensão e hegemonia do Google.

This thesis contributes to two completely unrelated debates in the economic literature, similar only in the relatively high degree of controversy characterizing each one. <p>The first part is methodological and macroeconomic in nature, addressing the question of whether the distribution of income across countries is converging (i.e. are the poor catching up to the rich?) or diverging (i.e. are we witnessing the formation of two exclusive clubs, one for poor countries and another one for rich countries?). Applications of the simple Markov model to this question have generated evidence in favor of the divergence hypothesis. In the first chapter, I critically review these results. I use statistical inference to show that the divergence results are not statistically robust, and I explain that this instability of the results comes from the application of a model for discrete data to data that is actually continuous. In the second chapter, I reposition the whole convergence-divergence debate by placing it in the context of Silverman’s classic survey of non-parametric density estimation techniques. This allows me to use the basic notions of fuzzy logic to adapt the simple Markov chain model to continuous data. When I apply the newly adapted Markov chain model to the cross-country distribution question, I find evidence against the divergence hypothesis, and this evidence is statistically robust. <p>The second part of the thesis is empirical and microeconomic in nature. I question whether observed differences between husbands’ and wives’ participation in labor markets are due to different preferences or to different constraints. My identification strategy is based on the idea that the more power an individual has relative to his/her partner, the more his/her actions will reflect his/her preferences. I use 2001 PSID data on cohabiting couples to estimate a simultaneous equations model of the spousal time allocation decision. My results confirm the stylized fact that specialization and trade does not explain time allocation for couples in which the wife is the primary breadwinner, and suggest that power could provide a more general explanation of the observations. My results show that wives with relatively more power choose to work more on the labor market and less at home, whereas husbands with more power choose to do the opposite. Since women start out from a lower level of labor market participation than men do, it would seem that spouses’ agree that the ideal mix of market work and housework lies somewhere between the husbands’ and the wives’ current positions. / Doctorat en sciences économiques, Orientation économie / info:eu-repo/semantics/nonPublished

L’objectif de cette thèse est l’étude d’un schéma numérique pour l’approximation des solutions d’équations différentielles doublement stochastiques rétrogrades (EDDSR). Durant les deux dernières décennies, plusieurs méthodes ont été proposées afin de permettre la résolution numérique des équations différentielles stochastiques rétrogrades standards. Dans cette thèse, on propose une extension de l’une de ces méthodes au cas doublement stochastique. Notre méthode numérique nous permet d’attaquer une large gamme d’équations aux dérivées partielles stochastiques (EDPS) nonlinéaires. Ceci est possible par le biais de leur représentation probabiliste en termes d’EDDSRs. Dans la dernière partie, nous étudions une nouvelle méthode des particules dans le cadre des études de protection en neutroniques. / The purpose of this thesis is to study a numerical method for backward doubly stochastic differential equations (BDSDEs in short). In the last two decades, several methods were proposed to approximate solutions of standard backward stochastic differential equations. In this thesis, we propose an extension of one of these methods to the doubly stochastic framework. Our numerical method allows us to tackle a large class of nonlinear stochastic partial differential equations (SPDEs in short), thanks to their probabilistic interpretation. In the last part, we study a new particle method in the context of shielding studies.

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Le contrôle explicite de la convergence des sommes convenablement normalisées de variables aléatoires, ainsi que l'étude du principe de déviations modérées associé à ces sommes constituent les thèmes centraux de cette thèse. Nous étudions principalement deux types de processus. Premièrement, nous nous intéressons aux processus indexés par un arbre binaire, aléatoire ou non. Ces processus ont été introduits dans la littérature afin d'étudier le mécanisme de la division cellulaire. Au chapitre 2, nous étudions les chaînes de Markov bifurcantes. Ces chaînes peuvent être vues comme une adaptation des chaînes de Markov "usuelles'' dans le cas où l'ensemble des indices à une structure binaire. Sous des hypothèses d'ergodicité géométrique uniforme et non-uniforme d'une chaîne de Markov induite, nous fournissons des inégalités de déviations et un principe de déviations modérées pour les chaînes de Markov bifurcantes. Au chapitre 3, nous nous intéressons aux processus bifurcants autorégressifs d'ordre p (). Ces processus sont une adaptation des processus autorégressifs linéaires d'ordre p dans le cas où l'ensemble des indices à une structure binaire. Nous donnons des inégalités de déviations, ainsi qu'un principe de déviations modérées pour les estimateurs des moindres carrés des paramètres "d'autorégression'' de ce modèle. Au chapitre 4, nous traitons des inégalités de déviations pour des chaînes de Markov bifurcantes sur un arbre de Galton-Watson. Ces chaînes sont une généralisation de la notion de chaînes de Markov bifurcantes au cas où l'ensemble des indices est un arbre de Galton-Watson binaire. Elles permettent dans le cas de la division cellulaire de prendre en compte la mort des cellules. Les hypothèses principales que nous faisons dans ce chapitre sont : l'ergodicité géométrique uniforme d'une chaîne de Markov induite et la non-extinction du processus de Galton-Watson associé. Au chapitre 5, nous nous intéressons aux modèles autorégressifs linéaires d'ordre 1 ayant des résidus corrélés. Plus particulièrement, nous nous concentrons sur la statistique de Durbin-Watson. La statistique de Durbin-Watson est à la base des tests de Durbin-Watson, qui permettent de détecter l'autocorrélation résiduelle dans des modèles autorégressifs d'ordre 1. Nous fournissons un principe de déviations modérées pour cette statistique. Les preuves du principe de déviations modérées des chapitres 2, 3 et 4 reposent essentiellement sur le principe de déviations modérées des martingales. Les inégalités de déviations sont établies principalement grâce à l'inégalité d'Azuma-Bennet-Hoeffding et l'utilisation de la structure binaire des processus. Le chapitre 5 est né de l'importance qu'a l'ergodicité explicite des chaînes de Markov au chapitre 3. L'ergodicité géométrique explicite des processus de Markov à temps discret et continu ayant été très bien étudiée dans la littérature, nous nous sommes penchés sur l'ergodicité sous-exponentielle des processus de Markov à temps continu. Nous fournissons alors des taux explicites pour la convergence sous exponentielle d'un processus de Markov à temps continu vers sa mesure de probabilité d'équilibre. Les hypothèses principales que nous utilisons sont : l'existence d'une fonction de Lyapunov et d'une condition de minoration. Les preuves reposent en grande partie sur la construction du couplage et le contrôle explicite de la queue du temps de couplage. / The explicit control of the convergence of properly normalized sums of random variables, as well as the study of moderate deviation principle associated with these sums constitute the main subjects of this thesis. We mostly study two sort of processes. First, we are interested in processes labelled by binary tree, random or not. These processes have been introduced in the literature in order to study mechanism of the cell division. In Chapter 2, we study bifurcating Markov chains. These chains may be seen as an adaptation of "usual'' Markov chains in case the index set has a binary structure. Under uniform and non-uniform geometric ergodicity assumptions of an embedded Markov chain, we provide deviation inequalities and a moderate deviation principle for the bifurcating Markov chains. In chapter 3, we are interested in p-order bifurcating autoregressive processes (). These processes are an adaptation of $p$-order linear autoregressive processes in case the index set has a binary structure. We provide deviation inequalities, as well as an moderate deviation principle for the least squares estimators of autoregressive parameters of this model. In Chapter 4, we dealt with deviation deviation inequalities for bifurcating Markov chains on Galton-Watson tree. These chains are a generalization of the notion of bifurcating Markov chains in case the index set is a binary Galton-Watson tree. They allow, in case of cell division, to take into account cell's death. The main hypothesis that we do in this chapter are : uniform geometric ergodicity of an embedded Markov chain and the non-extinction of the associated Galton-Watson process. In Chapter 5, we are interested in first-order linear autoregressive models with correlated errors. More specifically, we focus on the Durbin-Watson statistic. The Durbin-Watson statistic is at the base of Durbin-Watson tests, which allow to detect serial correlation in the first-order autoregressive models. We provide a moderate deviation principle for this statistic. The proofs of moderate deviation principle of Chapter 2, 3 and 4 are essentially based on moderate deviation for martingales. To establish deviation inequalities, we use most the Azuma-Bennet-Hoeffding inequality and the binary structure of processes. Chapter 6 was born from the importance that explicit ergodicity of Markov chains has in Chapter 2. Since explicit geometric ergodicity of discrete and continuous time Markov processes has been well studied in the literature, we focused on the sub-exponential ergodicity of continuous time Markov Processes. We thus provide explicit rates for the sub-exponential convergence of a continuous time Markov process to its stationary distribution. The main hypothesis that we use are : existence of a Lyapunov fonction and of a minorization condition. The proofs are largely based on the coupling construction and the explicit control of the tail of the coupling time.

En la actualidad, la Internet de las Cosas (Internet of Things, IoT) es una tecnología esencial para la próxima generación de sistemas inalámbricos. La conectividad es la base de IoT, y el tipo de acceso requerido dependerá de la naturaleza de la aplicación. Uno de los principales facilitadores del entorno IoT es la comunicación machine-to-machine (M2M) y, en particular, su enorme potencial para ofrecer conectividad ubicua entre dispositivos inteligentes. Las redes celulares son la elección natural para las aplicaciones emergentes de IoT y M2M. Un desafío importante en las redes celulares es conseguir que la red sea capaz de manejar escenarios de acceso masivo en los que numerosos dispositivos utilizan comunicaciones M2M. Por otro lado, los sistemas celulares han experimentado un tremendo desarrollo en las últimas décadas: incorporan tecnología sofisticada y nuevos algoritmos para ofrecer una amplia gama de servicios. El modelado y análisis del rendimiento de estas redes multiservicio es también una tarea desafiante que podría requerir un gran esfuerzo computacional. Para abordar los desafíos anteriores, nos centramos en primer lugar en el diseño y la evaluación de las prestaciones de nuevos mecanismos de control de acceso para hacer frente a las comunicaciones masivas M2M en redes celulares. Posteriormente nos ocupamos de la evaluación de prestaciones de redes multiservicio y proponemos una nueva técnica analítica que ofrece precisión y eficiencia computacional. Nuestro principal objetivo es proporcionar soluciones para aliviar la congestión en la red de acceso radio cuando un gran número de dispositivos M2M intentan conectarse a la red. Consideramos los siguientes tipos de escenarios: (i) los dispositivos M2M se conectan directamente a las estaciones base celulares, y (ii) forman grupos y los datos se envían a concentradores de tráfico (gateways) que les proporcionan acceso a la infraestructura. En el primer escenario, dado que el número de dispositivos añadidos a la red aumenta continuamente, esta debería ser capaz de manejar el considerable incremento en las solicitudes de acceso. El 3rd Generation Partnership Project (3GPP) ha propuesto el access class barring (ACB) como una solución práctica para el control de congestión en la red de acceso radio y la red troncal. El ajuste correcto de los parámetros de ACB de acuerdo con la intensidad del tráfico es crítico, pero cómo hacerlo de forma dinámica y autónoma es un problema complejo cuya solución no está recogida en las especificaciones del 3GPP. Esta tesis doctoral contribuye al análisis del rendimiento y al diseño de nuevos algoritmos que implementen efectivamente este mecanismo, y así superar los desafíos introducidos por las comunicaciones masivas M2M. En el segundo escenario, dado que la heterogeneidad de los dispositivos IoT y las arquitecturas celulares basadas en hardware imponen desafíos aún mayores para permitir una comunicación flexible y eficiente en los sistemas inalámbricos 5G, esta tesis doctoral también contribuye al diseño de software-defined gateways (SD-GWs) en una nueva arquitectura propuesta para redes inalámbricas definidas por software que se denomina SoftAir. Esto permite manejar tanto un gran número de dispositivos como el volumen de datos que estarán vertiendo en la red. Otra contribución de esta tesis doctoral es la propuesta de una técnica novedosa para el análisis de prestaciones de redes multiservicio de alta capacidad que se basa en un nuevo enfoque del modelizado analítico de sistemas que operan a diferentes escalas temporales. Este enfoque utiliza el análisis del transitorio de una serie de subcadenas absorbentes y lo denominamos absorbing Markov chain approximation (AMCA). Nuestros resultados muestran que para un coste computacional dado, AMCA calcula los parámetros de prestaciones habituales de un sistema con mayor precisión, en comparación con los resultados obtenidos por otr / Nowadays, Internet of Things (IoT) is an essential technology for the upcoming generation of wireless systems. Connectivity is the foundation for IoT, and the type of access required will depend on the nature of the application. One of the leading facilitators of the IoT environment is machine-to-machine (M2M) communication, and particularly, its tremendous potential to offer ubiquitous connectivity among intelligent devices. Cellular networks are the natural choice for emerging IoT and M2M applications. A major challenge in cellular networks is to make the network capable of handling massive access scenarios in which myriad devices deploy M2M communications. On the other hand, cellular systems have seen a tremendous development in recent decades; they incorporate sophisticated technology and algorithms to offer a broad range of services. The modeling and performance analysis of these large multi-service networks is also a challenging task that might require high computational effort. To address the above challenges, we first concentrate on the design and performance evaluation of novel access control schemes to deal with massive M2M communications. Then, we focus on the performance evaluation of large multi-service networks and propose a novel analytical technique that features accuracy and computational efficiency. Our main objective is to provide solutions to ease the congestion in the radio access or core network when massive M2M devices try to connect to the network. We consider the following two types of scenarios: (i) massive M2M devices connect directly to cellular base stations, and (ii) they form clusters and the data is forwarded to gateways that provide them with access to the infrastructure. In the first scenario, as the number of devices added to the network is constantly increasing, the network should handle the considerable increment in access requests. Access class barring (ACB) is proposed by the 3rd Generation Partnership Project (3GPP) as a practical congestion control solution in the radio access and core network. The proper tuning of the ACB parameters according to the traffic intensity is critical, but how to do so dynamically and autonomously is a challenging task that has not been specified. Thus, this dissertation contributes to the performance analysis and optimal design of novel algorithms to implement effectively this barring scheme and overcome the challenges introduced by massive M2M communications. In the second scenario, since the heterogeneity of IoT devices and the hardware-based cellular architectures impose even greater challenges to enable flexible and efficient communication in 5G wireless systems, this dissertation also contributes to the design of software-defined gateways (SD-GWs) in a new architecture proposed for wireless software-defined networks called SoftAir. The deployment of these SD-GWs represents an alternative solution aiming at handling both a vast number of devices and the volume of data they will be pouring into the network. Another contribution of this dissertation is to propose a novel technique for the performance analysis of large multi-service networks. The underlying complexity of the network, particularly concerning its size and the ample range of configuration options, makes the solution of the analytical models computationally costly. However, a typical characteristic of these networks is that they support multiple types of traffic flows operating at different time-scales. This time-scale separation can be exploited to reduce considerably the computational cost associated to determine the key performance indicators. Thus, we propose a novel analytical modeling approach based on the transient regime analysis, that we name absorbing Markov chain approximation (AMCA). For a given computational cost, AMCA finds common performance indicators with greater accuracy, when compared to the results obtained by other approximate methods proposed in the literature. / En l'actualitat, la Internet de les Coses (Internet of Things, IoT) és una tecnologia essencial per a la propera generació de sistemes sense fil. La connectivitat és la base d'IoT, i el tipus d'accés requerit dependrà de la naturalesa de l'aplicació. Un dels principals facilitadors de l'entorn IoT és la comunicació machine-to-machine (M2M) i, en particular, el seu enorme potencial per oferir connectivitat ubiqua entre dispositius intel · ligents. Les xarxes mòbils són l'elecció natural per a les aplicacions emergents de IoT i M2M. Un desafiament important en les xarxes mòbils que actualment está rebent molta atenció és aconseguir que la xarxa siga capaç de gestionar escenaris d'accés massiu en què una gran quantitat de dispositius utilitzen comunicacions M2M. D'altra banda, els sistemes mòbils han experimentat un gran desenvolupament en les últimes dècades: incorporen tecnologia sofisticada i nous algoritmes per oferir una àmplia gamma de serveis. El modelatge i análisi del rendiment d'aquestes xarxes multiservei és també un desafiament important que podria requerir un gran esforç computacional. Per abordar els desafiaments anteriors, en aquesta tesi doctoral ens centrem en primer lloc en el disseny i l'avaluació de les prestacions de nous mecanismes de control d'accés per fer front a les comunicacions massives M2M en xarxes cel · lulars. Posteriorment ens ocupem de l'avaluació de prestacions de xarxes multiservei i proposem una nova tècnica analítica que ofereix precisió i eficiència computacional. El nostre principal objectiu és proporcionar solucions per a alleujar la congestió a la xarxa d'accés ràdio quan un gran nombre de dispositius M2M intenten connectar-se a la xarxa. Considerem els dos tipus d'escenaris següents: (i) els dispositius M2M es connecten directament a les estacions base cel · lulars, i (ii) formen grups i les dades s'envien a concentradors de trànsit (gateways) que els proporcionen accés a la infraestructura. En el primer escenari, atès que el nombre de dispositius afegits a la xarxa augmenta contínuament, aquesta hauria de ser capaç de gestionar el considerable increment en les sol · licituds d'accés. El 3rd Generation Partnership Project (3GPP) ha proposat l'access class barring (ACB) com una solució pràctica per al control de congestió a la xarxa d'accès ràdio i la xarxa troncal. L'ajust correcte dels paràmetres d'ACB d'acord amb la intensitat del trànsit és crític, però com fer-ho de forma dinàmica i autònoma és un problema complex, la solució del qual no està recollida en les especificacions del 3GPP. Aquesta tesi doctoral contribueix a l'anàlisi del rendiment i al disseny de nous algoritmes que implementen efectivament aquest mecanisme, i així superar els desafiaments introduïts per les comunicacions massives M2M en les xarxes mòbils actuals i futures. En el segon escenari, atès que l'heterogeneïtat dels dispositius IoT i les arquitectures cel · lulars basades en hardware imposen desafiaments encara més grans per permetre una comunicació flexible i eficient en els sistemes sense fil 5G, aquesta tesi doctoral també contribueix al disseny de software-defined gateways (SD-GWS) en una nova arquitectura proposada per a xarxes sense fils definides per programari que s'anomena SoftAir. Això permet gestionar tant un gran nombre de dispositius com el volum de dades que estaran abocant a la xarxa. Una altra contribució d'aquesta tesi doctoral és la proposta d'una tècnica innovadora per a l'anàlisi de prestacions de xarxes multiservei d'alta capacitat que es basa en un nou enfocament del modelitzat analític de sistemes que operen a diferents escales temporals. Aquest enfocament utilitza l'anàlisi del transitori d'una sèrie de subcadenes absorbents i l'anomenem absorbing Markov chain Approximation (AMCA). Els nostres resultats mostren que per a un cost computacional donat, AMCA calcula els paràmetres de prestacions habituals d / Tello Oquendo, LP. (2018). Design and Performance Analysis of Access Control Mechanisms for Massive Machine-to-Machine Communications in Wireless Cellular Networks [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/107946