Statistics and Probability Commons^™

On The Gumbel-Weibull{Cauchy} Distribution, Jennifer D. Pippin

Theses, Dissertations and Capstones

Developing new statistical distributions and seeking higher flexibility in modeling different shapes of data remain a strong emphasis in research. The T-R{Y } framework, introduced in [3], utilizes three statistical distributions in order to generate a new distribution. Many research papers appeared in literature to develop distributions based on the T-R{Y } framework. In this thesis, a member of the T-R{Y } framework, namely the Gumbel-Weibull{Cauchy} (GWC), is introduced. Statistical properties of the GWC are studied, such as the quantile function, the hazard function, transformations, Shannon entropy, the …

Floquet Theory For First-Order Delay Equations And An Application To Height Stabilization Of A Drone’S Flight, Martin Bohner, Alexander Domoshnitsky, Oleg Kupervasser, Alex Sitkin

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we proposed a version of the Floquet theory for delay differential equations. We demonstrated that very natural assumptions for control in technical applications can lead us to a one-dimensional fundamental system. This approach allowed researchers to work with classical methods used in the case of ordinary differential equations. On this basis, new original unexpected results on the exponential stability were proposed. For example, in the equation x' (4)+a(t)x(t—-T(7)) = 0, t € [0, co), we avoided the assumption on the smallness of the product sup,j9,.) 41 SUP;< {9,00) TD) < 3/2 for asymptotic stability. We obtained that in the case of w-periodic coefficient and delay, the fact that the period w was situated in a corresponding interval can lead to exponential stability. We then applied our new tests of stability to the stabilization of a drone's flight, where smallness of the noted above product could not be achieved from a technical point of view. For an equation with periodic coefficient and delay, we got a formula of the solution's representation on the semiaxis.

Gompertz Distribution On Time Scales, Wasiu Sule

Theses, Dissertations and Capstones

We shall investigate Gompertz dynamic equations within the context of time scales calculus, by exploring the mathematical foundations and applications of the Gompertz model, which is commonly used to describe growth phenomena in various fields such as biology and economics. This research seeks to analyze the Gompertz cumulative distribution functions (CDF) and probability density functions (PDF) across different time scales, including the real numbers R and integer multiples hN. Probability techniques will be used to derive the CDF and PDF associated with the Gompertz dynamic equations, and we will examine how varying the time scale impacts the characteristics …

A Unified Concept Of Periodicity On Any Time Scale And Applications, Martin Bohner, Jaqueline G. Mesquita, Sabrina H. Streipert

Mathematics and Statistics Faculty Research & Creative Works

We introduce a novel definition of periodicity on arbitrary time scales, dependent on a strictly increasing and differentiable function. This removes the commonly used and restrictive assumption of a periodic time scale to define periodic functions. Our new definition furthermore allows for a wider class of functions to be studied using the theory of periodic systems. After providing crucial properties of these periodic functions, such as the translation invariance of integrals of periodic functions, we apply the concept of this new periodicity to linear dynamic equations. We provide necessary and sufficient conditions for a linear dynamic equation to have such …

The Discrete Generalized Proportional Fractional Derivative, Martin Bohner, Rajrani Gupta

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we have introduced a discrete generalized proportional fractional derivative and generated Riemann-Liouville and Caputo discrete generalized proportional fractional derivatives. The Laplace transforms of the discrete generalized proportional fractional derivatives and integrals are also calculated.

Empirical Vulnerability Function Development Based On The Damage Caused By The 2014 Chiang Rai Earthquake, Thailand, Patcharavadee Hong, Masashi Matsuoka

Institute for Innovation & Entrepreneurship Publications

Seismic hazards in Thailand are frequently overlooked in disaster management planning, leading to insufficient research and significant economic losses during earthquake events. The 2014 Chiang Rai earthquake exposed critical vulnerabilities in Thailand's building practices due to widespread non-compliance with building codes and limited preparedness. This exposure prompted the development of empirical vulnerability functions using loss data from 15,031 damaged residences. The study analyzed government compensation records, which were standardized using replacement cost metrics. Three distinct models were developed through probabilistic and possibilistic modeling approaches. Residual analysis demonstrated the superior performance of the possibilistic approach, with the Possibilistic-based Vulnerability Function achieving …

Predicting Superconducting Critical Temperature From Composition-Derived Features: A Transparent Linear And Regularized Regression Study, Md Ahiduzzaman

Data Science and Data Mining

We study prediction of superconducting critical temperature (Tc) from 81 composition-derived descriptors across 21,263 materials. To keep the analysis transparent and repro- ducible, we focus on linear models: Ordinary Least Squares (OLS), Ridge, Lasso, and Elastic Net (ENet). All models share a single evaluation protocol (5-fold cross-validation with standardized inputs) and are compared on RMSE, MAE, and R2. On this feature set, OLS attains the best cross-validated performance (RMSE = 17.6 K, MAE = 13.3 K , R2 = 0.735), with Lasso/ENet essentially tied next (RMSE ≈ 17.7 K , R2 ≈ 0.734); Ridge underperforms (RMSE = 18.9 K , …

Comparative Analysis Of Lasso, Ridge, And Elastic Net For Variable Selection In High-Dimensional Maize Data, Md Ahiduzzaman

Data Science and Data Mining

In high-dimensional genomic data analysis, traditional linear regression techniques often struggle due to the presence of a large number of predictor variables relative to observations. Penalized regression methods such as LASSO, Ridge, and Elastic Net have emerged as effective solutions by imposing regularization, which helps in managing multicollinearity and enhancing prediction accuracy. This study applies these techniques to the Maize dataset to model the time to male flowering, selecting relevant genetic markers as predictors. Our findings suggest that Elastic Net is particularly effective for high-dimensional data with correlated variables, achieving a balance between prediction accuracy and variable selection. The results …

Enhanced Kneser-Type Oscillation Criteria For Second-Order Functional Quasilinear Dynamic Equations On Time Scales, Taher S. Hassan, Elvan Akın, Bassant M. El-Matary, Ioan Lucian Popa, Mouataz Billah Mesmouli, Ismoil Odinaev, Akbar Ali

Mathematics and Statistics Faculty Research & Creative Works

This work presents new Kneser-type oscillation criteria for second-order quasilinear functional dynamic equations defined on arbitrary unbounded above time scales. Our approach employs the Riccati transformation technique in conjunction with the integral averaging method. The results show a significant improvement over recent Kneser-type oscillation criteria. We provided several illustrative examples to highlight the importance of our findings.

An Evaluation On The Uncertainty For The Routine Of Dosimetry Calibration At The National Secondary Standard Dosimetry Laboratory, Albania, Klotilda Nikaj

International Journal of Nuclear Security

Every employer must, in relation to any work with ionizing radiation that they undertake, take all necessary steps to restrict so far as is reasonably practicable the extent to which their employees and other persons are exposed to ionizing radiation. This goal leads to an increased awareness about the proper maintenance and annual calibration of the personal dosimeters to ensure an accurate and precise radiation dose. The present work has described the performance of the radiation system of the ¹³⁷Cs source at the National Secondary Standard Dosimetry Laboratory (SSDL), located at the Institute of Applied Nuclear Physics at the …

Gaps In Knowledge: Topological Insights Into The Structure Of Science, Gavin Engelstad

Mathematics, Statistics, and Computer Science Honors Projects

Understanding scientific development is essential to ascertaining the mechanisms leading us into the future. Building this understanding requires both methodological developments and empirical research. This thesis contributes in both aspects using a topological approach to examine scientific knowledge. The first section presents a new algorithm to find optimal cycle representatives for homological features in complex networks, a context for which we demonstrate existing algorithms can be inadequate. The second section applies a number of topological methods, including our cycle optimization algorithm, to data on individual scientific fields, demonstrating the value of topological approaches and highlighting new insights about how science …

Handwritten Digit Recognition Using Machine Learning Classifiers, Md Ahiduzzaman

Data Science and Data Mining

This project explores and compares the performance of various machine learning classifiers for handwritten digit recognition using the MNIST dataset. The classifiers include Logistic Regression, k-Nearest Neighbors, and Convolutional Neural Networks. Each classifier is evaluated based on accuracy, precision, recall, F1-score, and confusion matrix analysis.

Statistical Analysis Of Climate Trends And Variability In Tarrant County Using Annual, Decade, And Three-Decade Time Periods, Quinnton Debolt

Earth & Environmental Sciences Theses - Archive

This study is a statistical analysis of climate trends within the Dallas-Fort Worth metroplex according to several time-scale models to understand how the climate for the locality has changed and to provide a basis for projections of what future climate might look like. Trends in mean temperature and precipitation for North Central Texas generally correlate with corresponding global trends linked to natural variability and anthropogenic-induced climate change. Temperature rises in this region annually by 0.08°C and by 0.22°C for a three-decade average. Seasonal increases in three-decadal averages of temperature for North Central Texas relative to the average of the reference …

A New Formulation Of Hardy-Type Dynamic Inequalities On Time Scales, Martin Bohner, Irena Jadlovská, Ahmed I. Saied

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we introduce a novel formulation of dynamic Hardy-type inequalities on a time scale, motivated by a recently established convexity approach in the Haar measure. The classical Hardy inequality is refined so that the classical Lebesgue-measure constant is replaced by the sharp constant 1. We obtain time-scale analogues on finite intervals with best constants, and, for nonincreasing and nondecreasing functions, reversed inequalities with explicit weights described by incomplete β-functions. To establish our results, we employ two distinct time scales and apply the chain rule, together with the substitution rule, the derivative of inverse functions, and Fubini's theorem for …

Analysis Of Errors In The Management Of Cutaneous Disorders, Robert J. Pariser, Sarah Alnaif

Department Dermatology Faculty Publications

In this study, we prospectively and retrospectively evaluated the occurrence of errors in the management of cutaneous disorders from patient visits and medical records in a single dermatology practice in southeast Virginia over a 3-year period (June 2020-July 2023). Providers should be able to improve diagnostic accuracy by utilizing established rapid bedside diagnostic techniques.

The Economic And Environmental Impact Of Shinkansen And High-Speed Rail Infrastructure: A Comparative Analysis Of Economic Growth And Carbon Emissions Reduction, Dillan R. Victory

SPARK Symposium Presentations

The development of Japan's high-speed rail system, the Shinkansen, has played a pivotal role in the country's post-war economic resurgence. Introduced in 1964 with the Tokaidō Shinkansen, this transformative infrastructure investment significantly reduced travel times, bolstered economic activity around station hubs, and facilitated regional development by enabling urban decentralization. This paper explores the long-term economic benefits of high-speed rail, including its impact on land value, business expansion, and carbon emissions. The case study of the Linear Chuo Shinkansen, Japan's latest maglev project, underscores both the economic promise and the political resistance to expansion, particularly in regions such as Shizuoka.

Using …

Generalizations Of Finiteness Conditions And Extension Monads In Algebras With Infinitely Many Or Infinitary Operations, Danielle Christienne Bowerman

Doctoral Dissertations

In this work, we extend the results of finiteness conditions and extension monads found in Insall from finitely many finitary operations to infinitely many finitary operations, as well as touching on infinitary operations. We also examine varieties of algebras, including the notion of strong varieties introduced in Insall, and common constructions of extension monads in varieties of algebras. We see that for finite collections of algebras of the same signature, the extension monad operation on a variety of algebras commutes with the direct product operation, and all retractions from an enlargement or extension monad are trivial. We also see that …

Beyond Homogeneity: Exploring Causal Heterogeneity In Psychopathology, Philip B. Vinh

Theses and Dissertations

Traditional models in psychiatric research often impose assumptions of causal homogeneity, treating population-level associations as reflective of uniform underlying mechanisms. This dissertation challenges that assumption by introducing statistical and machine learning frameworks designed to detect and model causal heterogeneity in the development of psychopathology. Central to this approach is the advancement of finite mixture structural equation modeling (FM-SEM) to identify latent subgroups characterized by distinct, and sometimes opposing, causal pathways.

The dissertation comprises three integrated empirical studies. The first introduces mixDoC, a finite mixture extension of the classical Direction of Causation (DoC) model applied to twin data, enabling the detection …

Predictive Inference For Ion Concentration With Machine Learning And Bayesian Methods, Alexandra B. Ulbing

Theses and Dissertations

Ultraviolet--visible (UV--Vis) spectroscopy produces high-dimensional signals that are strongly collinear, shift with concentration, and exhibit heteroskedastic, non-Gaussian noise. These features make supervised regression from spectra to ionic concentrations statistically challenging and limit the reliability of methods that assume linear structure or homoscedastic errors.

This dissertation develops two complementary frameworks for prediction and uncertainty quantification in UV--Vis spectroscopic regression: (1) frequentist stacked ensembles combined with distribution-free conformal prediction, and (2) Bayesian hierarchical modeling and Bayesian stacking. Together, they provide a unified view of model-based and distribution-free uncertainty across nickel and nickel--cobalt datasets.

The frequentist component builds ensembles of Functional Data Analysis …

Predicting Capture And Survival Probabilities Of The Arizona Tiger Salamander: A Comparison Of Capture-Recapture Models, Brittney Nelson

Murray State Theses and Dissertations

Capture-recapture models are essential tools for estimating population dynamics in ecological studies. A fundamental component of these models is the capture history matrix, which records individual detection over time and serves as the basis for estimating survival and capture probabilities. This presentation explores three statistical approaches to these estimations: the Cormack-Jolly-Seber (CJS) model, the Hidden Markov Model (HMM) for CJS, and the Bayesian CJS model. The CJS model provides a likelihood-based framework for estimation, and the HMM CJS incorporates latent states into the model to account for uncertainty in detection. The Bayesian CJS extends this same analysis by integrating prior …