The work presented in this thesis studies the load and loadeffects of traffic loads on railway bridges. The increasedknowledge of the traffic loads, simulated using fieldmeasurements of actual trains, are employed in a reliabilityanalysis in an attempt at upgrading existing railwaybridges. The study utilises data from a weigh-in-motion site whichrecords, for each train, the train speed, the loads from eachaxle and the axle spacings. This data of actual trainconfigurations and axle loads are portrayed as moving forcesand then used in computer simulations of trains crossing twodimensional simply supported bridges at constant speed. Onlysingle track short to medium span bridges are considered in thethesis. The studied load effect is the moment at mid-span. Fromthe computer simulations the moment history at mid-span isobtained. The load effects are analysed by two methods, the first isthe classical extreme value theory where the load effect ismodelled by the family of distributions called the generalisedextreme value distribution (GEV). The other method adopts thepeaks-over-threshold method (POT) where the limiting family ofdistributions for the heights to peaks-over-threshold is theGeneralised Pareto Distribution (GPD). The two models aregenerally found to be a good representation of the data. The load effects modelled by either the GEV or the GPD arethen incorporated into a reliability analysis in order to studythe possibility of raising allowable axle loads on existingSwedish railway bridges. The results of the reliabilityanalysis show that they are sensitive to the estimation of theshape parameter of the GEV or the GPD. While the study is limited to the case of the ultimate limitstate where the effects of fatigue are not accounted for, thefindings show that for the studied cases an increase inallowable axle load to 25 tonnes would be acceptable even forbridges built to the standards of 1940 and designed to LoadModel A of that standard. Even an increase to both 27.5 and 30tonnes appears to be possible for certain cases. It is alsoobserved that the short span bridges ofapproximately fourmetres are the most susceptible to a proposed increase inpermissible axle load. <b>Keywords:</b>bridge, rail, traffic load, load effect,dynamic amplification factor, extreme value theory,peaks-over-threshold, reliability theory, axle loads, fielddata.

The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. This means, roughly speaking, that thereis a non-negligible probability for very large or extremeoutcomes to occur. Such models are useful in applicationsincluding insurance, finance and telecommunications networks.It is shown how regular variation of the marginals, or theincrements, of a stochastic process implies regular variationof functionals of the process. Moreover, the associated tailbehavior in terms of a limit measure is derived. The second part of the thesis studies problems related toparameter estimation in stochastic models with long memory.Emphasis is on the estimation of the drift parameter in somestochastic differential equations driven by the fractionalBrownian motion or more generally Volterra-type processes.Observing the process continuously, the maximum likelihoodestimator is derived using a Girsanov transformation. In thecase of discrete observations the study is carried out for theparticular case of the fractional Ornstein-Uhlenbeck process.For this model Whittle’s approach is applied to derive anestimator for all unknown parameters.

optimizationover a discrete number of random variables. In this paperwe extend this theory from the discrete to the continuous case, andconsider the limiting distribution of the location of the best offer asthe number of offers tends to infinity.Given a set   Rd of possible offers we seek a distribution over ,the argmax measure of the best offer. It depends on , the samplingdistribution of offer locations, and a measure index , which assignsto each point x 2  a probability distribution of offers.This problem is closely related to argmax theory of marked pointprocesses, altough we consider deterministic sequences of points inspace, to allow for greater generality. We first define a finite sampleargmax measure and then give conditions under which it converges asthe number of offers tends to infinity.To this end, we introduce a max-field of best offers and use continuityproperties of this field to calculate the argmax measure. Wedemonstrate the usefulness of the method by giving explicit formulasfor the limiting argmax distribution for a large class of models, includingexponential independent offers with a deterministic, additivedisturbance term. Finally, we illustrate the theory by simulations.

(None) Technical Summary of Thesis: The topic of my thesis is currency crisis. Currency crises have been a recurrent feature of the international economy from the invention of paper money. They are not confined to particular economies or specific region. They take place in developed, emerging, and developing countries and are spread all over the globe. Countries that experience currency crises face economic losses that can be huge and disruptive. However, the exacted toll is not only financial and economic, but also human, social, and political. It is clear that the currency crisis is a real threat to financial stability and economic prosperity. The main objective of this thesis is to analyze the determinants of currency crises for twenty OECD countries and South Africa from 1970 through 1998. It systematically examines the role of economic fundamentals and contagion in the origins of currency crises and empirically attempts to identify the channels through which the crises are being transmitted. It also examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. The first chapter identifies the episodes of currency crisis in our data set. Determining true crisis periods is a vital step in the empirical studies and has direct impact on the reliability of their estimations and the relevant policy implications. We define a period as a crisis episode when the Exchange Market Pressure (EMP) index, which consists of changes in exchange rates, reserves, and interest rates, exceeds a threshold. In order to minimize the concerns regarding the accuracy of identified crisis episodes, we apply extreme value theory, which is a more objective approach compared to other methods. In this chapter, we also select the reference country, which a country’s currency pressure index should be built around, in a more systematic way rather than by arbitrary choice or descriptive reasoning. The second chapter studies the probability of a currency exiting a tranquil state into a crisis state. There is an extensive literature on currency crises that empirically evaluate the roots and causes of the crises. Despite the interesting results of the current empirical literature, only very few of them account for the influence of time on the probability of crises. We use duration models that rigorously incorporate the time factor into the likelihood functions and allow us to investigate how the amount of time that a currency has already spent in the tranquil state affects the stability of a currency. Our findings show that high values of volatility of unemployment rates, inflation rates, contagion factors (which mostly work through trade channels), unemployment rates, real effective exchange rate, trade openness, and size of economy increases the hazard of a crisis. We make use of several robustness checks, including running our models on two different crisis episodes sets that are identified based on monthly and quarterly type spells. The third chapter examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. As in our previous paper, duration analysis is our methodology to study the probability of a currency crisis occurrence under different exchange rate regimes and capital mobility policies. The third chapter finds that there is a significant link between the choice of exchange rate regime and the incidence of currency crises in our sample. Nevertheless, the results are sensitive to the choice of the de facto exchange rate system. Moreover, in our sample, capital control policies appear to be helpful in preventing low duration currency crises. The results are robust to a wide variety of sample and models checks.

(None) Technical Summary of Thesis: The topic of my thesis is currency crisis. Currency crises have been a recurrent feature of the international economy from the invention of paper money. They are not confined to particular economies or specific region. They take place in developed, emerging, and developing countries and are spread all over the globe. Countries that experience currency crises face economic losses that can be huge and disruptive. However, the exacted toll is not only financial and economic, but also human, social, and political. It is clear that the currency crisis is a real threat to financial stability and economic prosperity. The main objective of this thesis is to analyze the determinants of currency crises for twenty OECD countries and South Africa from 1970 through 1998. It systematically examines the role of economic fundamentals and contagion in the origins of currency crises and empirically attempts to identify the channels through which the crises are being transmitted. It also examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. The first chapter identifies the episodes of currency crisis in our data set. Determining true crisis periods is a vital step in the empirical studies and has direct impact on the reliability of their estimations and the relevant policy implications. We define a period as a crisis episode when the Exchange Market Pressure (EMP) index, which consists of changes in exchange rates, reserves, and interest rates, exceeds a threshold. In order to minimize the concerns regarding the accuracy of identified crisis episodes, we apply extreme value theory, which is a more objective approach compared to other methods. In this chapter, we also select the reference country, which a country’s currency pressure index should be built around, in a more systematic way rather than by arbitrary choice or descriptive reasoning. The second chapter studies the probability of a currency exiting a tranquil state into a crisis state. There is an extensive literature on currency crises that empirically evaluate the roots and causes of the crises. Despite the interesting results of the current empirical literature, only very few of them account for the influence of time on the probability of crises. We use duration models that rigorously incorporate the time factor into the likelihood functions and allow us to investigate how the amount of time that a currency has already spent in the tranquil state affects the stability of a currency. Our findings show that high values of volatility of unemployment rates, inflation rates, contagion factors (which mostly work through trade channels), unemployment rates, real effective exchange rate, trade openness, and size of economy increases the hazard of a crisis. We make use of several robustness checks, including running our models on two different crisis episodes sets that are identified based on monthly and quarterly type spells. The third chapter examines the links between the incidence of currency crises and the choice of exchange rate regimes as well as the impact of capital market liberalization policies on the occurrence of currency crises. As in our previous paper, duration analysis is our methodology to study the probability of a currency crisis occurrence under different exchange rate regimes and capital mobility policies. The third chapter finds that there is a significant link between the choice of exchange rate regime and the incidence of currency crises in our sample. Nevertheless, the results are sensitive to the choice of the de facto exchange rate system. Moreover, in our sample, capital control policies appear to be helpful in preventing low duration currency crises. The results are robust to a wide variety of sample and models checks.

This dissertation investigates the implications of using the Advanced Measurement Approaches (AMA) as a method to assess operational risk capital charges for banks and insurance companies within Basel II paradigms and with regard to U.S. regulations. Operational risk has become recognized as a major risk class because of huge operational losses experienced by many financial firms over the last past decade. Unlike market risk, credit risk, and insurance risk, for which firms and scholars have designed efficient methodologies, there are few tools to help analyze and quantify operational risk. The new Basel Revised Framework for International Convergence of Capital Measurement and Capital Standards (Basel II) gives substantial flexibility to internationally active banks to set up their own risk assessment models in the context of the Advanced Measurement Approaches. The AMA developed in this thesis uses actuarial loss models complemented by the extreme value theory to determine the empirical probability distribution function of the overall capital charge in terms of various classes of copulas. Publicly available operational risk loss data set is used for the empirical exercise.

<p>The work presented in this thesis studies the load and loadeffects of traffic loads on railway bridges. The increasedknowledge of the traffic loads, simulated using fieldmeasurements of actual trains, are employed in a reliabilityanalysis in an attempt at upgrading existing railwaybridges.</p><p>The study utilises data from a weigh-in-motion site whichrecords, for each train, the train speed, the loads from eachaxle and the axle spacings. This data of actual trainconfigurations and axle loads are portrayed as moving forcesand then used in computer simulations of trains crossing twodimensional simply supported bridges at constant speed. Onlysingle track short to medium span bridges are considered in thethesis. The studied load effect is the moment at mid-span. Fromthe computer simulations the moment history at mid-span isobtained.</p><p>The load effects are analysed by two methods, the first isthe classical extreme value theory where the load effect ismodelled by the family of distributions called the generalisedextreme value distribution (GEV). The other method adopts thepeaks-over-threshold method (POT) where the limiting family ofdistributions for the heights to peaks-over-threshold is theGeneralised Pareto Distribution (GPD). The two models aregenerally found to be a good representation of the data.</p><p>The load effects modelled by either the GEV or the GPD arethen incorporated into a reliability analysis in order to studythe possibility of raising allowable axle loads on existingSwedish railway bridges. The results of the reliabilityanalysis show that they are sensitive to the estimation of theshape parameter of the GEV or the GPD.</p><p>While the study is limited to the case of the ultimate limitstate where the effects of fatigue are not accounted for, thefindings show that for the studied cases an increase inallowable axle load to 25 tonnes would be acceptable even forbridges built to the standards of 1940 and designed to LoadModel A of that standard. Even an increase to both 27.5 and 30tonnes appears to be possible for certain cases. It is alsoobserved that the short span bridges ofapproximately fourmetres are the most susceptible to a proposed increase inpermissible axle load.</p><p><b>Keywords:</b>bridge, rail, traffic load, load effect,dynamic amplification factor, extreme value theory,peaks-over-threshold, reliability theory, axle loads, fielddata.</p>

<p>The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. This means, roughly speaking, that thereis a non-negligible probability for very large or extremeoutcomes to occur. Such models are useful in applicationsincluding insurance, finance and telecommunications networks.It is shown how regular variation of the marginals, or theincrements, of a stochastic process implies regular variationof functionals of the process. Moreover, the associated tailbehavior in terms of a limit measure is derived.</p><p>The second part of the thesis studies problems related toparameter estimation in stochastic models with long memory.Emphasis is on the estimation of the drift parameter in somestochastic differential equations driven by the fractionalBrownian motion or more generally Volterra-type processes.Observing the process continuously, the maximum likelihoodestimator is derived using a Girsanov transformation. In thecase of discrete observations the study is carried out for theparticular case of the fractional Ornstein-Uhlenbeck process.For this model Whittle’s approach is applied to derive anestimator for all unknown parameters.</p>

This study consists of developing descriptive, parametric, linear and non-linear statistical models for such natural phenomena as hurricanes, lightning, flooding, red tide and volcanic fallout. In the present study, the focus of research is determining the stochastic nature of phenomena in the environment. These statistical models are necessary to address the variability of nature and the misgivings of the deterministic models, particularly when considering the necessity for man to estimate the occurrence and prepare for the aftermath.The relationship between statistics and physics looking at the correlation between wind speed and pressure versus wind speed and temperature play a significant role in hurricane prediction. Contrary to previous studies, this study indicates that a drop in pressure is a result of the storm and less a cause. It shows that temperature is a key indicator that a storm will form in conjunction with a drop in pressure. This study demonstrates a model that estimates the wind speed within a storm with a high degree of accuracy. With the verified model, we can perform surface response analysis to estimate the conditions under which the wind speed is maximized or minimized. Additional studies introduce a model that estimates the number of lightning strikes dependent on significantly contributing factors such as precipitable water, the temperatures within a column of air and the temperature range. Using extreme value distribution and historical data we can best fit flood stages, and obtain profiling estimate return periods. The natural logarithmic count of Karenia Brevis was used to homogenize the variance and create the base for an index of the magnitude of an outbreak of Red Tide. We have introduced a logistic growth model that addresses the subject behavior as a function of time and characterizes the growth rate of Red Tide. This information can be used to develop strategic plans with respect to the health of citizens and to minimize the economic impact. Studying the bivariate nature of tephra fallout from volcanoes, we analyze the correlation between the northern and eastern directions of a topological map to find the best possible probabilistic characterization of the subject data.

The dissertation focuses on developing statistical models in environmental and life sciences. The Generalized Extreme Value distribution is used to model annual monthly maximum rainfall data from 44 locations in Florida. Time dependence of the rainfall data is incorporated into the model by assuming the location parameter to be a function of time, both linear and quadratic. Estimates and confidence intervals are obtained for return levels of return periods of 10, 20, 50, and 100 years. Locations are grouped into statistical profiles based on their similarities in return level graphs for all locations, and locations within each climatic zone. A family of extreme values distributions is applied to model simulated maximum drug concentration (Cmax) data of an anticoagulant drug. For small samples (n <̲ 100) data exhibited bimodality. The results of investigating a mixture of two extreme value distributions to model such bimodal data using two-parameter Gumbel, Pareto and Weibu ll concluded that a mixture of two Weibull distributions is the only suitable FTSel.For large samples , Cmax data are modeled using the Generalized Extreme Value, Gumbel, Weibull, and Pareto distributions. These results concluded that the Generalized Extreme Value distribution is the only suitable model. A system of random differential equations is used to investigate the drug concentration behavior in a three-compartment pharmacokinetic model which describes coumermycin's disposition. The rate constants used in the differential equations are assumed to have a trivariate distribution, and hence, simulated from the trivariate truncated normal probability distribution. Numerical solutions are developed under different combinations of the covariance structure and the nonrandom initial conditions. We study the dependence effect that such a pharmacokinetic system has among the three compartments as well as the effect of variance in identifying the concentration behavior in each compartment. We identify the time delays in each compartment. We extend these models to incorporate the identified time delays. We provide the graphical display of the time delay effects on the drug concentration behavior as well as the comparison of the deterministic behavior with and without the time delay, and effect of different sets of time delay on deterministic and stochastic behaviors.