Physical Sciences and Mathematics Commons^™

Recent Advances In Accumulating Priority Queues, Na Li

Electronic Thesis and Dissertation Repository

This thesis extends the theory underlying the Accumulating Priority Queue (APQ) in three directions. In the first, we present a multi-class multi-server accumulating priority queue with Poisson arrivals and heterogeneous services. The waiting time distributions for different classes have been derived. A conservation law for systems with heterogeneous servers has been studied. We also investigate an optimization problem to find the optimal level of heterogeneity in the multi-server system. Numerical investigations through simulation are carried out to validate the model.

We next focus on a queueing system with Poisson arrivals, generally distributed service times and nonlinear priority accumulation functions. We …

A Novel Method For Assessing Co-Monotonicity: An Interplay Between Mathematics And Statistics With Applications, Danang T. Qoyyimi

Electronic Thesis and Dissertation Repository

Numerous problems in econometrics, insurance, reliability engineering, and statistics rely on the assumption that certain functions are monotonic, which may or may not be true in real life scenarios. To satisfy this requirement, from the theoretical point of view, researchers frequently model the underlying phenomena using parametric and semi-parametric families of functions, thus effectively specifying the required shapes of the functions. To tackle these problems in a non-parametric way, when the shape cannot be specified explicitly but only estimated approximately, we suggest indices for measuring the lack of monotonicity in functions. We investigate properties of these indices and offer convenient …

Probabilistic Reasoning In Cosmology, Yann Benétreau-Dupin

Electronic Thesis and Dissertation Repository

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology.

The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such arguments …

On The Estimation Of Intracluster Correlation For Time-To-Event Outcomes In Cluster Randomized Trials, Sumeet Kalia

Electronic Thesis and Dissertation Repository

Cluster randomized trials (CRTs) involve the random assignment of intact social units rather than independent subjects to intervention groups. Time-to-event outcomes often are endpoints in CRTs where the intracluster correlation coefficient (ICC) serves as a descriptive parameter to assess the similarity among outcomes in a cluster. However, estimating the ICC in CRTs with time-to-event outcomes is a challenge due to the presence of censored observations. The ICC is estimated for two CRTs using the censoring indicators and observed outcomes.

A simulation study explores the effect of administrative censoring on estimating the ICC. Results show that the ICC estimators derived from …

Completely Monotone And Bernstein Functions With Convexity Properties On Their Measures, Shen Shan

Electronic Thesis and Dissertation Repository

The concepts of completely monotone and Bernstein functions have been introduced near one hundred years ago. They find wide applications in areas ranging from stochastic L\'{e}vy processes and complex analysis to monotone operator theory. They have well-known Bernstein and L\'{e}vy-Khintchine integral representations through which there are one-to-one correspondences between them and Radon measures on $[0,\infty)$ or $(0,\infty)$, respectively. In this thesis, we investigate subclasses of completely monotone and Bernstein functions with various convexity properties on their measures. These subclasses have intriguing applications in probability theories and convex analysis.

The convexity properties we investigate include convexity, harmonic convexity and $\beta$-convexity of …

Tropical Cyclone Wind Hazard Assessment For Southeast Part Of Coastal Region Of China, Sihan Li

Electronic Thesis and Dissertation Repository

Tropical cyclone (TC) or typhoon wind hazard and risk are significant for China. The return period value of the maximum typhoon wind speed is used to characterize the typhoon wind hazard and assign wind load in building design code. Since the historical surface observations of typhoon wind speed are often scarce and of short period, the typhoon wind hazard assessment is often carried out using the wind field model and TC track model. For a few major cities in the coastal region of mainland China, simple or approximated wind field models and a circular subregion method (CSM) have been used …

On The Dual Risk Models, Chen Yang

Electronic Thesis and Dissertation Repository

Abstract This thesis focuses on developing and computing ruin-related quantities that are potentially measurements for the dual risk models which was proposed to describe the annuity-type businesses from the perspective of the collective risk theory in 1950’s. In recent years, the dual risk models are revisited by many researchers to quantify the risk of the similar businesses as the annuity-type businesses. The major extensions included in this thesis consist of two aspects: the first is to search for new ruin-related quantities that are potentially indices of the risk for well-established dual models; the other aspect is to generalize the settings …

Healthy And Unhealthy Statistics: Examining The Impact Of Erroneous Statistical Analyses In Health-Related Research, Britney Allen

Electronic Thesis and Dissertation Repository

Sound statistical analyses are essential to the advancement of medicine. Although certainly not always the case, far too many publications are based on weak or inappropriate statistical methodology, leading to questionable results. Statistical reporting guidelines and standards for research are being introduced which should help curb this problem. Wide recognition of the need for statistical methodologies aligned with research questions and study designs, and the impact when this is not the case, would help prevent this problem. In this thesis, I illustrate the consequences of erroneous statistical analyses on data from an observational study on Multiple Sclerosis and I investigate …

Quantitative Techniques For Spread Trading In Commodity Markets, Mir Hashem Moosavi Avonleghi

Electronic Thesis and Dissertation Repository

This thesis investigates quantitative techniques for trading strategies on two commodities, the difference of whose prices exhibits a long-term historical relationship known as mean-reversion. A portfolio of two commodity prices with very similar characteristics, the spread may be regarded as a distinct process from the underlying price processes so deserves to be modeled directly. To pave the way for modeling the spread processes, the fundamental concepts, notions, properties of commodity markets such as the forward prices, the futures prices, and convenience yields are described. Some popular commodity pricing models including both one and two factor models are reviewed. A new …

Online Nonparametric Estimation Of Stochastic Differential Equations, Xin Wang

Electronic Thesis and Dissertation Repository

The advent of the big data era presents new challenges and opportunities for those managing portfolios, both of assets and of risk exposures, for the financial industry. How to cope with the volume of data to quickly extract actionable information is becoming more crucial than ever before. This information can be used, for example, in pricing various financial products or in calculating risk exposures to meet (ever changing) regulatory requirements.

Stochastic differential equations are often used to model the risk factors in finance. Given the presumption of a functional form for the coefficients of these equations, the required parameters can …

Extensions Of The Cross-Entropy Method With Applications To Diffusion Processes And Portfolio Losses, Alexandre Scott

Electronic Thesis and Dissertation Repository

Rare event simulation is a crucial part of simulations. In financial mathematics, the study of rare events appear naturally when we consider risk measures such as the conditional value at risk. This thesis is composed of three related papers treating the rare event simulations subject: the first paper addresses rare event simulations using for diffusion processes, the second paper addresses rare event simulations for the normal and the Student t-copula model while the last paper addresses rare event simulations for a portfolio model where there is a correlation structure between the loss-given-default and the probability of default.