Over the last 20 to 30 years, there have been a significant number of statistical methods proposed for analyzing crash data. Traffic crashes are characterized as random and independent discrete non-negative events. Crash data have often been shown to exhibit over-dispersion. Therefore, the Negative Binomial (NB) is the preferred and widely used model to analyze this kind of data. Although NB model is very popular in traffic safety area, it still has limitations modeling crash data especially when crash data are characterized by low sample mean and small sample size. The main research objective of this thesis is to develop a new statistical method namely, Poisson-Weibull (PW) Generalized Linear Model (GLM) to analyze vehicle crash data and to evaluate its modeling performance at different dispersion levels. This study makes use of both simulated and observed data for accomplishing the research objectives. The PW model is the mixture of Poisson and Weibull distributions. In this research, the statistical characteristics of the PW model were well defined and the parameters were estimated using a Bayesian approach. The PW model was initially evaluated using a series of simulated data for different dispersion levels. It was found that the PW model was able to reproduce and capture the true parameter values with high accuracy. After the initial analysis using the simulated data, the PW GLM was applied to two observed datasets and compared with the NB model. The goodness-of-fit (GOF) tests and model comparisons showed that the PW model performed as well as the NB model. Therefore, the PW model can be considered as an innovative and promising alternative for analyzing crash data.

Esta dissertação tem como objetivo apresentar um caso específico de Interpolação da Estrutura a Termo da Taxa de Juros (ETTJ) com base no processo estocástico que de- termina a taxa de juros, o qual é aqui denominado por interpolação estrutural. Este método estrutural permite a calibração das curvas de desconto e de rendimento, por meio do ajuste dos parâmetros do modelo generalizado Black-Karasinski sob a hipótese de não arbitragem. São apresentados três métodos distintos de calibragem. O primeiro deles é constituído pela solução numérica do sistema de equações que satisfaz a hipótese de não arbitragem. O segundo método remete-se a inversão dos parâmetros do modelo de forma exata, a partir da definição da curva de rendimento. O terceiro e último método apresenta uma solução aproximada a partir de um problema reduzido. Mostramos que os métodos são equivalentes quando se utiliza a mesma definição para a curva de rendimentos. A importância deste resultado reside no desenvolvimento de algoritmos de fácil implemen- tação computacional e na possibilidade de usar esse método de interpolação com base em um modelo de determinação da taxa de juros em trabalhos empíricos de previsão e determinação da estrutura a termo da taxa de juros. / This paper aims to present a special case of interpolation of the Term Structure of In- terest Rates based on the stochastic process that determines the interest rate, which is here called by structural interpolation. This structural method allows the calibration discounts and yields curves adjusted through the parameters of the generalized Black-Karasinski model under the assumption of no arbitrage. Three distinct methods of calibration are presented. The first consists of the numerical solution of the system of equations that satisfes the hypothesis of no arbitrage. The second method refers to the inversion of the parameters model, from the definition of the yield curve. The third and last method presents an approximate solution from a smaller problem. We show that the three meth- ods are equivalent when using the same definition for the yield curve. The importance of this result lies in the development of algorithms for easy computational implementation and the possibility of using this interpolation method based on a model for determining the rate of interest for empirical prediction and determination of the term structure of interest rates.

Esta dissertação tem como objetivo apresentar um caso específico de Interpolação da Estrutura a Termo da Taxa de Juros (ETTJ) com base no processo estocástico que de- termina a taxa de juros, o qual é aqui denominado por interpolação estrutural. Este método estrutural permite a calibração das curvas de desconto e de rendimento, por meio do ajuste dos parâmetros do modelo generalizado Black-Karasinski sob a hipótese de não arbitragem. São apresentados três métodos distintos de calibragem. O primeiro deles é constituído pela solução numérica do sistema de equações que satisfaz a hipótese de não arbitragem. O segundo método remete-se a inversão dos parâmetros do modelo de forma exata, a partir da definição da curva de rendimento. O terceiro e último método apresenta uma solução aproximada a partir de um problema reduzido. Mostramos que os métodos são equivalentes quando se utiliza a mesma definição para a curva de rendimentos. A importância deste resultado reside no desenvolvimento de algoritmos de fácil implemen- tação computacional e na possibilidade de usar esse método de interpolação com base em um modelo de determinação da taxa de juros em trabalhos empíricos de previsão e determinação da estrutura a termo da taxa de juros. / This paper aims to present a special case of interpolation of the Term Structure of In- terest Rates based on the stochastic process that determines the interest rate, which is here called by structural interpolation. This structural method allows the calibration discounts and yields curves adjusted through the parameters of the generalized Black-Karasinski model under the assumption of no arbitrage. Three distinct methods of calibration are presented. The first consists of the numerical solution of the system of equations that satisfes the hypothesis of no arbitrage. The second method refers to the inversion of the parameters model, from the definition of the yield curve. The third and last method presents an approximate solution from a smaller problem. We show that the three meth- ods are equivalent when using the same definition for the yield curve. The importance of this result lies in the development of algorithms for easy computational implementation and the possibility of using this interpolation method based on a model for determining the rate of interest for empirical prediction and determination of the term structure of interest rates.

Esta dissertação tem como objetivo apresentar um caso específico de Interpolação da Estrutura a Termo da Taxa de Juros (ETTJ) com base no processo estocástico que de- termina a taxa de juros, o qual é aqui denominado por interpolação estrutural. Este método estrutural permite a calibração das curvas de desconto e de rendimento, por meio do ajuste dos parâmetros do modelo generalizado Black-Karasinski sob a hipótese de não arbitragem. São apresentados três métodos distintos de calibragem. O primeiro deles é constituído pela solução numérica do sistema de equações que satisfaz a hipótese de não arbitragem. O segundo método remete-se a inversão dos parâmetros do modelo de forma exata, a partir da definição da curva de rendimento. O terceiro e último método apresenta uma solução aproximada a partir de um problema reduzido. Mostramos que os métodos são equivalentes quando se utiliza a mesma definição para a curva de rendimentos. A importância deste resultado reside no desenvolvimento de algoritmos de fácil implemen- tação computacional e na possibilidade de usar esse método de interpolação com base em um modelo de determinação da taxa de juros em trabalhos empíricos de previsão e determinação da estrutura a termo da taxa de juros. / This paper aims to present a special case of interpolation of the Term Structure of In- terest Rates based on the stochastic process that determines the interest rate, which is here called by structural interpolation. This structural method allows the calibration discounts and yields curves adjusted through the parameters of the generalized Black-Karasinski model under the assumption of no arbitrage. Three distinct methods of calibration are presented. The first consists of the numerical solution of the system of equations that satisfes the hypothesis of no arbitrage. The second method refers to the inversion of the parameters model, from the definition of the yield curve. The third and last method presents an approximate solution from a smaller problem. We show that the three meth- ods are equivalent when using the same definition for the yield curve. The importance of this result lies in the development of algorithms for easy computational implementation and the possibility of using this interpolation method based on a model for determining the rate of interest for empirical prediction and determination of the term structure of interest rates.

An efficient application and development of renewable energy sources is one of the most important contribution to the energetic balance of the human society. Anyhow, statistical model of the renewable energy market, which would fundamentally explain relevant economical rules related to these perspective energetic resources, is not clearly known up to now. Nevertheless, the relevant statistical data concerning application of solar energy (photovoltaic and thermo-solar heating) are available for the last twenty years. Based on the economic models, statistical data concerning sales of photovoltaic models and thermo-solar collectors sales have been analysed in this work. It has been shown that the model of constant elasticity predicts an exponential increase which will slow down when a certain level of annual cumulative sales was reached. The model of constant elasticity was found to be successful to interpret past sales data. In the approach of variable elasticity model the parameter of the elasticity has been modified as a function of variables such as market volume, price and time through the statistical evaluation. It enabled to calculate initial, saturation and competitive market conditions, as well. Whereas the constant elasticity demand model describes exponential growth of sales and installations, which was characteristic for the beginning of the application of these renewable resources of energy, the variable elasticity demand model describes a more realistic situation, where cumulative sales either increase or decrease and prices vary subsequently. Simple growth model of unlimited demand based on the growing sales is not realistic and could not be feasible in the long term. The market elasticity could be understood as a real economical parameter representing percentual market increase or decrease at a given time; in the variable demand elasticity model, the constant elasticity is replaced by a function of a market volume, price and time. In this case, we can estimate model parameters for the different market conditions: growth, saturation and decrease. The function representing the capital adequacy in the generalized market model has also been deliberated. Statistical models have been used to determine cumulative sales and market prices of photovoltaic modules and thermo-solar collectors. Moreover, model parameters have been used for the calculation of the realized photovoltaic and thermo solar projects' capital adequacy on the renewable energy market. By using model parameters, renewable energy market forecast up to 2020 has been estimated. We have used generalized market model to credibly estimate future renewable energy market until 2020; as well as extend model parameterization on other resources of renewable energy (water and wind, geothermal sources, biomass) and set prices of energy produced from these renewable sources. Potential energetic savings have been estimated for households (apartments and private houses), who can be relevant consumers of energy from renewable sources. We have performed statistical findings on randomly selected files, where we have reached a real energy consumption, to prove this. This research allowed us to perform a real estimate of a renewable energy contribution to the total energy balance. We have successfully proved that linearly growing capital adequacy function, with an annual growth between 2.5% and 3.0%, is reflecting the renewable energy market sufficiently and is fully in line with an average growth of the total energy consumption. Renewable energy share on the total energy balance will grow substantially to reach a level of 15% in 2015 on the world market and a level of 8% in the Czech Republic for the same period with a perspective to reach a level of 11% in 2020 respectively. Assuming this level of renewable energy on the total production will lead to a decrease of CO2 emissions by three million of tones in 2015 and by four million of tones in 2020. Final reach of this status quo is fully predicted by our statistical model for renewable energy market.

A new suboptimal guidance law design approach for aerospace vehicles is proposed in this thesis, followed by an advanced control design for supersonic air-breathing engines. The guidance law is designed using the newly developed Generalized Model Predictive Static Programming (G-MPSP), which is based on the continuous time nonlinear optimal control framework. The key feature of this technique is one-time backward propagation of a small-dimensional weighting matrix dynamics, which is used to update the entire control history. This key feature, as well as the fact that it leads to a static optimization problem, lead to its computational efficiency. It has also been shown that the existing model predictive static programming (MPSP), which is based on the discrete time framework, is a special case of G-MPSP. The G-MPSP technique is further extended to incorporate ‘input inequality constraints’ in a limited sense using the penalty function philosophy. Next, this technique has been developed also further in a ‘flexible final time’ framework to converge rapidly to meet very stringent final conditions with limited number of iterations. Using the G-MPSP technique in a flexible final time and input inequality constrained formulation, a suboptimal guidance law for a solid motor propelled carrier launch vehicle is successfully designed for a hypersonic mission. This guidance law assures very stringent final conditions at the injection point at the end of the guidance phase for successful beginning of the hypersonic vehicle operation. It also ensures that the angle of attack and structural load bounds are not violated throughout the trajectory. A second-order autopilot has been incorporated in the simulation studies to mimic the effect of the inner-loops on the guidance performance. Simulation studies with perturbations in the thrust-time behaviour, drag coefficient and mass demonstrate that the proposed guidance can meet the stringent requirements of the hypersonic mission. The G-MPSP technique in a fixed final time and input inequality constrained formulation has also been used for optimal guidance of an aerospace vehicle propelled by supersonic air-breathing engine, where the resulting thrust can be manipulated by managing the fuel flow and nozzle area (which is not possible in solid motors). However, operation of supersonic air-breathing engines is quite complex as the thrust produced by the engine is a result of very complex nonlinear combustion dynamics inside the engine. Hence, to generate the desired thrust, accounting for a fairly detailed engine model, a dynamic inversion based nonlinear state feedback control design has been carried out. The objective of this controller is to ensure that the engine dynamically produces the thrust that tracks the commanded value of thrust generated from the guidance loop as closely as possible by regulating the fuel flow rate. Simultaneously, by manipulating throat area of the nozzle, it also manages the shock wave location in the intake for maximum pressure recovery with sufficient margin for robustness. To filter out the sensor and process noises and to estimate the states for making the control design operate based on output feedback, an extended Kalman filter (EKF) based state estimation design has also been carried out and the controller has been made to operate based on estimated states. Moreover, independent control designs have also been carried out for the actuators so that their response can be faster. In addition, this control design becomes more challenging to satisfy the imposed practical constraints like fuel-air ratio and peak combustion temperature limits. Simulation results clearly indicate that the proposed design is quite successful in assuring the desired performance of the air-breathing engine throughout the flight trajectory, i.e., both during the climb and cruise phases, while assuring adequate pressure margin for shock wave management.