Statistics and Probability Commons^™

The Martingale Approach To Financial Mathematics, Jordan M. Rowley

Master's Theses

In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In …

Forward Selection Via Distance Correlation, Ty Adams

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.

The Long-Run Effects Of Tropical Cyclones On Infant Mortality, Isabel Miranda

Master's Theses

In the United States alone, each tropical cyclone causes an average of $14.6 billion worth of damages. In addition to the destruction of physical infrastructure, natural disasters also negatively impact human capital formation. These losses are often more difficult to observe, and therefore, are over looked when quantifying the true costs of natural disasters. One particular effect is an increase in infant mortality rates, an important indicator of a country’s general socioeconomic level. This paper utilizes a model created by Anttila-Hughes and Hsiang, that takes advantage of annual variation in tropical cyclones using annual spatial average maximum wind speeds and …

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.

Market Research On Student Concert Attendance At Bgsu's College Of Musical Arts, Mary Solomon

Honors Projects

Bowling Green State University boasts a well established College of Musical Arts which holds concerts performed by esteemed faculty, prestigious guest artists, and students. The school hosts these events in Kobacker Hall and Bryan Recital Hall which can accommodate up to 800 and 250 audience members, respectively. However, performances in Kobacker hall only fill one- fourth of the 800 seats, on average. Why is this so? This project aims to investigate the factors that influence students’ decisions to attend concerts at the College of Musical Arts (CMA). By methodology of survey research and statistical analysis, this project will look into …

Black Swamp Pub And Bistro Analysis, Sara Aniol

Honors Projects

The Black Swamp Pub and Bistro is a full-service restaurant located in the Union on the Bowling Green State University Campus. We mainly do sit-down service, but we also do take-out orders and have a full bar with draft beers as well as mixed drinks. Our menu tends to change a lot, with new additions as well as some of the items being deleted. My goal of this project is to try to give some insight on the patterns that are too big to see with day-to-day operations as well as give some recommendations for the future that is backed …

Sampling Studies For Longitudinal Functional Data, Toni Jassel

Theses, Dissertations and Culminating Projects

We study the data setting consisting of functional data sets repeatedly observed over time. The focus is on the dynamic prediction of the future trajectory for a subject. Regression methods based on dynamic functional models are used for dynamic prediction of individual trajectories. We propose strategies for the selection of the study sampling design in the context of longitudinal functional data. An application to simulated child growth data is presented. The height-for-age z-score (HAZ) was the response variable in the functional dynamic models for prediction. The intent was to recommend four months for removal in our initial historic data set. …

Statistical Modeling Of Count Data With Over-Dispersion Or Zero-Inflation Problems, Chengxin Zhang

Theses, Dissertations and Culminating Projects

In this study, we will analyze a supply retailing company’s data to model the relationship between their customer’s past purchase behavior to predict their future online purchase behavior. The data was divided into time periods from 2016: P1-P6(January 31st to July 30th) and P7(July 31st to August 27th ). Based on customer’s past purchase information from the P1-P6 period, such as money spent, number of cart additions, transactions type, number of unique purchase dates, number of unique purchase skus, number of page views, number browse dates, company size, and number of products purchased, we aim to find if these information …

Generalizations Of The Arcsine Distribution, Rebecca Rasnick

Electronic Theses and Dissertations

The arcsine distribution looks at the fraction of time one player is winning in a fair coin toss game and has been studied for over a hundred years. There has been little further work on how the distribution changes when the coin tosses are not fair or when a player has already won the initial coin tosses or, equivalently, starts with a lead. This thesis will first cover a proof of the arcsine distribution. Then, we explore how the distribution changes when the coin the is unfair. Finally, we will explore the distribution when one person has won the first …

Dynamic Attribute-Level Best Worst Discrete Choice Experiments, Amanda Working, Mohammed Alqawba, Norou Diawara

Mathematics & Statistics Faculty Publications

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are …

Simulation As A Predictor In Probability, Xiaona Zhou

Publications and Research

In this study, we simulate bivariate normal data. We gain intuition about the bivariate normal distribution by comparing the generated data to the associated bivariate normal density surface. We also get results about covariance and correlation. We will use tools from linear algebra to discuss transformations of random normal vectors, and the use of contours.

Contributions To Mcmc Methods In Constrained Domains With Applications To Neuroimaging, Sharang Chaudhry

UNLV Theses, Dissertations, Professional Papers, and Capstones

Markov chain Monte Carlo (MCMC) methods form a rich class of computational techniques that help its user ascertain samples from target distributions when direct sampling is not possible or when their closed forms are intractable. Over the years, MCMC methods have been used in innumerable situations due to their flexibility and generalizability, even in situations involving nonlinear and/or highly parametrized models. In this dissertation, two major works relating to MCMC methods are presented.

The first involves the development of a method to identify the number and directions of nerve fibers using diffusion-weighted MRI measurements. For this, the biological problem is …

A Gene-Based Recessive Diplotype Exome Scan Discovers Fgf6, A Novel Hepcidin-Regulating Iron-Metabolism Gene, Shicheng Guo, Shuai Jiang, Narendranath Epperla, Yanyun Ma, Mehdi Maadooliat, Zhan Ye, Brent Olson, Minghua Wang, Terrie Kitchner, Jeffrey Joyce, Peng An, Fudi Wang, Robert Strenn, Joseph J. Mazza, Jennifer K. Meece, Wenyu Wu, Li Jin, Judith A. Smith, Jiucan Wang, Steven J. Schrodi

Mathematical and Statistical Science Faculty Research and Publications

Standard analyses applied to genome-wide association data are well designed to detect additive effects of moderate strength. However, the power for standard genome-wide association study (GWAS) analyses to identify effects from recessive diplotypes is not typically high. We proposed and conducted a gene-based compound heterozygosity test to reveal additional genes underlying complex diseases. With this approach applied to iron overload, a strong association signal was identified between the fibroblast growth factor–encoding gene, FGF6, and hemochromatosis in the central Wisconsin population. Functional validation showed that fibroblast growth factor 6 protein (FGF-6) regulates iron homeostasis and induces transcriptional regulation of hepcidin. …

A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

The classical unconditional exact p-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact p-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate the …

Historical Study Of The Relationship Between The Federal Funds Rate And The Inflation Rate, Aaron Wilkins

Undergraduate External Publications

It is believed that in order to control high inflation rates, the Federal Reserve Bank (“the Fed”) increases the federal funds rate and when the inflation rate gets low, the Fed takes the opposite approach. (The federal funds rate is a rate of interest that banks charge each other to lend funds and stay above the reserve requirement, set by the government.) This project examines the relationship between the federal funds rate and the inflation rate. Sixty-five years of historical inflation rates and federal funds rates were used as the basis for this exploration. Because a time lag between the …

Accurate Inference For Repeated Measures In High Dimensions, Xiaoli Kong, Solomon W. Harrar

Mathematics and Statistics: Faculty Publications and Other Works

This paper proposes inferential methods for high-dimensional repeated measures in factorial designs. High-dimensional refers to the situation where the dimension is growing with sample size such that either one could be larger than the other. The most important contribution relates to high-accuracy of the methods in the sense that p-values, for example, are accurate up to the second-order. Second-order accuracy in sample size as well as dimension is achieved by obtaining asymptotic expansion of the distribution of the test statistics, and estimation of the parameters of the approximate distribution with second-order consistency. The methods are presented in a unified and …

Unified Methods For Feature Selection In Large-Scale Genomic Studies With Censored Survival Outcomes, Lauren Spirko-Burns, Karthik Devarajan

COBRA Preprint Series

One of the major goals in large-scale genomic studies is to identify genes with a prognostic impact on time-to-event outcomes which provide insight into the disease's process. With rapid developments in high-throughput genomic technologies in the past two decades, the scientific community is able to monitor the expression levels of tens of thousands of genes and proteins resulting in enormous data sets where the number of genomic features is far greater than the number of subjects. Methods based on univariate Cox regression are often used to select genomic features related to survival outcome; however, the Cox model assumes proportional hazards …

Drones And “Ghost Guns”: Unregulated Legal Space, Tori Bodine

Research on Capitol Hill

Law enforcement agencies are fighting a two - pronged battle when it comes to emerging technologies: keeping up with new ways criminals are using technology and developing effective ways to combat these innovations, while balancing these challenges against preserving the individual liberties of law - abiding citizens. This conflict is especially apparent with regard to criminal use of commercial drones and the developing fringe market surrounding homemade untraceable firearms (“ghost guns”).

Large Scale Dynamical Model Of Macrophage/Hiv Interactions, Sean T. Bresnahan, Matthew M. Froid

UNO Student Research and Creative Activity Fair

Properties emerge from the dynamics of large-scale molecular networks that are not discernible at the individual gene or protein level. Mathematical models - such as probabilistic Boolean networks - of molecular systems offer a deeper insight into how these emergent properties arise. Here, we introduce a non-linear, deterministic Boolean model of protein, gene, and chemical interactions in human macrophage cells during HIV infection. Our model is composed of 713 nodes with 1583 interactions between nodes and is responsive to 38 different inputs including signaling molecules, bacteria, viruses, and HIV viral particles. Additionally, the model accurately simulates the dynamics of over …

Smale Strategies For The $N$-Person Iterated Prisoner's Dilemma, Ethan Akin, Sławomir Plaskacz, Joanna Zwierzchowska

Mathematics and Statistics Faculty Research & Creative Works

Adapting methods introduced by Steven Smale, we describe good strategies for a symmetric version of the Iterated Prisoner's Dilemma with n players.

The Odd Log-Logistic Gompertz Lifetime Distribution: Properties And Applications, Morad Alizadeh, Saeid Tahmasebi, Mohammad Reza Kazemi, Hamideh Siyamar Arabi Nejad, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we introduce a new three-parameter generalized version of the Gompertz model called the odd log-logistic Gompertz (OLLGo) distribution. It includes some well-known lifetime distributions such as Gompertz (Go) and odd log-logistic exponential (OLLE) as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function and …

Sustainable Energy Governance In South Tyrol (Italy): A Probabilistic Bipartite Network Model, Jessica Belest, Laura Secco, Elena Pisani, Alberto Caimo

Articles

At the national scale, almost all of the European countries have already achieved energy transition targets, while at the regional and local scales, there is still some potential to further push sustainable energy transitions. Regions and localities have the support of political, social, and economic actors who make decisions for meeting existing social, environmental and economic needs recognising local specificities.

These actors compose the sustainable energy governance that is fundamental to effectively plan and manage energy resources. In collaborative relationships, these actors share, save, and protect several kinds of resources, thereby making energy transitions deeper and more effective.

This research …

Improving Vix Futures Forecasts Using Machine Learning Methods, James Hosker, Slobodan Djurdjevic, Hieu Nguyen, Robert Slater

SMU Data Science Review

The problem of forecasting market volatility is a difficult task for most fund managers. Volatility forecasts are used for risk management, alpha (risk) trading, and the reduction of trading friction. Improving the forecasts of future market volatility assists fund managers in adding or reducing risk in their portfolios as well as in increasing hedges to protect their portfolios in anticipation of a market sell-off event. Our analysis compares three existing financial models that forecast future market volatility using the Chicago Board Options Exchange Volatility Index (VIX) to six machine/deep learning supervised regression methods. This analysis determines which models provide best …

Critical Fault-Detecting Time Evaluation In Software With Discrete Compound Poisson Models, Min-Hsiung Hsieh, Shuen-Lin Jeng, Paul Kvam

Department of Math & Statistics Faculty Publications

Software developers predict their product’s failure rate using reliability growth models that are typically based on nonhomogeneous Poisson (NHP) processes. In this article, we extend that practice to a nonhomogeneous discrete-compound Poisson process that allows for multiple faults of a system at the same time point. Along with traditional reliability metrics such as average number of failures in a time interval, we propose an alternative reliability index called critical fault-detecting time in order to provide more information for software managers making software quality evaluation and critical market policy decisions. We illustrate the significant potential for improved analysis using wireless failure …

Extensions Of Schauder's And Darbo's Fixed Point Theorems, Zhaocai Hao, Martin Bohner, Junjun Wang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, some new extensions of Schauder's and Darbo's fixed point theorems are given. As applications of the main results, the existence of global solutions for first-order nonlinear integro-differential equations of mixed type in a real Banach space is investigated.

Exploring The Variance Of The Sample Variance Through Estimation And Simulation, Christina Stradwick

Theses, Dissertations and Capstones

In this thesis, we examine properties of the variance of the sample variance, which we will denote V (S ² ). We derive a formula for this variance and show that it only depends on the sample size, variance, and kurtosis of the underlying distribution. We also derive the maximum likelihood estimators for this parameter, V^ˆ (S ² ), under the normal, exponential, Bernoulli, and Poisson distributions and end the thesis with simulations demonstrating the distributions of these estimators.

Comparison Of Green's Functions For A Family Of Boundary Value Problems For Fractional Difference Equations, Paul W. Eloe, Catherine Kublik, Jeffrey T. Neugebauer

Mathematics Faculty Publications

In this paper, we obtain sign conditions and comparison theorems for Green's functions of a family of boundary value problems for a Riemann-Liouville type delta fractional difference equation. Moreover, we show that as the length of the domain diverges to infinity, each Green's function converges to a uniquely defined Green's function of a singular boundary value problem.

Counting And Coloring Sudoku Graphs, Kyle Oddson

Mathematics and Statistics Dissertations, Theses, and Final Project Papers

A sudoku puzzle is most commonly a 9 × 9 grid of 3 × 3 boxes wherein the puzzle player writes the numbers 1 - 9 with no repetition in any row, column, or box. We generalize the notion of the n² × n² sudoku grid for all n ∈ ℤ^≥2 and codify the empty sudoku board as a graph. In the main section of this paper we prove that sudoku boards and sudoku graphs exist for all such n; we prove the equivalence of [3]'s construction using unions and products of graphs to the definition of …

A Second Order Bdf Numerical Scheme With Variable Steps For The Cahn-Hilliard Equation, Wenbin Chen, Xiaoming Wang, Yue Yan, Zhuying Zhang

Mathematics and Statistics Faculty Research & Creative Works

We present and analyze a second order in time variable step BDF2 numerical scheme for the Cahn-Hilliard equation. the construction relies on a second order backward difference, convex-splitting technique and viscous regularizing at the discrete level. We show that the scheme is unconditionally stable and uniquely solvable. in addition, under mild restriction on the ratio of adjacent time-steps, an optimal second order in time convergence rate is established. the proof involves a novel generalized discrete Gronwall-type inequality. as far as we know, this is the first rigorous proof of second order convergence for a variable step BDF2 scheme, even in …

10. Corrections To Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

Corrections for the provided by the authors for Design and Analysis of Experiments.