Other Statistics and Probability Commons^™

(R2152) New Bivariate Type-2 Gumbel Distribution Based On The Farlie-Gumbel-Morgenstern Copula: Properties And Its Application In Survival Analysis, Muneeb Javed, Said Farooq Shah, Muhammad Osama, Muhammad Atif, Muhammad Farooq

Applications and Applied Mathematics: An International Journal (AAM)

We introduce a new bivariate probability distribution, termed the Bivariate FGM Type-2 Gumbel Distribution, constructed by combining the Farlie–Gumbel–Morgenstern (FGM) copula with the Type-2 Gumbel marginal distributions. This proposed distribution provides a flexible framework for modeling bivariate data and offers a viable alternative to several existing bivariate distributions, especially in scenarios where capturing dependence between variables is crucial. The theoretical properties of the distribution are thoroughly explored. We derive the marginal and conditional distributions, conditional expectations, moment generating function, and product moments. Procedures for random number generation from the distribution are discussed. Reliability-based characteristics, such as the survival function and …

Human Capital, Immigration, And Growth: A State-Level Dynamic Panel Study, William R. Cooper

Graduate Theses and Dissertations (2019 - present)

This study examines whether who immigrates, rather than how many, matters for state economic growth in the United States. It integrates a policy-relevant proxy for skill (H-1B approvals) into an augmented Solow framework that separates immigration's quantity channel from its human capital channel and estimates dynamic effects in a balanced quarterly panel of 50 states (2010 to 2023 ). The empirical strategy estimates a two-step difference GMM Arellano-Bond model that reinforces identification using a double/debiased machine learning (DML) variant that orthogonalizes high-dimensional nuisance components via cross-fitting. This design targets the distinct roles of immigrant headcount versus skill in per capita …

Exploring The Impact Of Statistics Course Modality On Student Learning: A Mixed Methods Approach, Becky Kelleman

Electronic Theses and Dissertations

The importance of statistical literacy has become increasingly evident, as individuals grapple with interpreting statistics to inform critical decisions. Despite the recognized significance of statistical literacy, challenges persist in both educators’ and students’ efforts to navigate the complexities of statistics education. The purpose of this study is to explore the impact of different course modalities on undergraduate students’ academic performance in introductory statistics courses. Using Social Cognitive Theory (SCT) as a theoretical framework, this research aims to shed light on the complex dynamics influencing statistical literacy attainment. By addressing gaps and inconsistencies in the current literature, this study seeks to …

Performance Of The Two Sample Likelihood Ratio Test Under A Nested Dirichlet: A Simulation Study, Edwina Agyeman

Electronic Theses and Dissertations

Compositional data analysis (CoDA) addresses multivariate data constrained to a constant sum, such as proportions or percentages. Originating from early warnings regarding misinterpretation by Pearson (1897), the field was formalized by John Aitchison in 1986, whose foundational work remains highly influential. Over time, new modeling techniques and visualization tools have advanced the field, as noted by Greenacre et al. More recently, Turner et al. proposed an approach based on the Nested Dirichlet Distribution (NDD), which accommodates more flexible dependence structures than the standard Dirichlet model. This thesis builds on the methodology of Turner et al. Chapter 1 introduces the nature …

How’S It Growing? Tools For Observing Snow And Sea Ice In A Changing Arctic Ocean, Ian Alexander Raphael

Dartmouth College Ph.D Dissertations

September Arctic sea ice extent has diminished by roughly 50% in the 45 years since satellite observations began. The Arctic Ocean may experience ice-free summers within the next decade, with implications for habitat, resource extraction, geopolitics, and local and global climate change. To predict how Arctic sea ice will change in the future, we need to understand its behavior in the present. In situ sea ice mass balance measurements (snow accumulation, ice growth, snow and ice surface melt, and bottom melt) are essential for studying the processes driving rapid changes in the ice pack, and for validating remote sensing measurements …

A Study On Fuzzy Time-Series And Its Applications To Stock Price Forecasting, Takeshi Stormer

University Honors Theses

Fuzzy mathematics looks to incorporate the vagueness that exists within the real world, specifically regarding imprecise classes, or non-numerical information expressed as "linguistic" variables. Since most traditional mathematical theories do not have the ability to be applied with the exactness that is otherwise seen in mathematics. As such, there had been many applications of fuzzy mathematics throughout many different fields of mathematics, including that of forecasting. By exploring the fundamentals of fuzzy mathematics, including fuzzy sets, operations of fuzzy sets, the surface level introduction to fuzzy logic, fuzzy relations, operations of fuzzy relations, and fuzzy time-series, this work looks to …

Babies, Babes, And Bayes: Modeling Mother-Infant Feedings With Bayesian Multilevel Hidden Markov Models, Zachary G. Felix

Master's Theses

Understanding the interaction between mother and baby during feeding is critical for the long-term development health of the baby. Overfeeding can lead to later obesity, while underfeeding can lead to malnutrition. In a recent study, the behaviors exhibited by mother-infant dyads across multiple ages of infants have been observed and coded according to the Baby Behaviors when Satiated (BABES) coding scheme. However, creating models using the data obtained from this coding is no simple task since the data coding is continuous, multivariate, and longitudinal in nature. The specific model utilized for these data is a hidden Markov model, since there …

Clusters, Trends, And Choices: Feature Selection In Interactive Statistical Graphics, Dylan Le

Master's Theses

Exploratory data analysis (EDA) is a method for uncovering the structure and key characteristics of data, often through the use of statistical graphics. These visual tools can reveal patterns and trends, and their effectiveness can be enhanced through interactivity. By enabling users to filter data, zoom, and toggle visual features, interactive plots can accelerate and enrich the EDA process. This study extends a previous graphical study by incorporating an interactive framework. Using a statistical lineup protocol with two target patterns (a linear trend and a clustering trend) participants interacted with plots by toggling various aesthetic features, including cluster coloring, ellipses …

Statistical Investigations Of Strategies In The Game Ecosystem, Dylan Li

Master's Theses

This work provides a probability-based analysis of strategies in the board game Ecosystem. Ecosystem is a turn-based multiplayer tiling game, where players take turns picking a wildlife card from a limited pool of cards then placing that card on their personal 4x5 grid. The objective of the game is to place the wildlife cards to maximize your score, as each card’s scoring condition depends on the presence or absence of certain cards surrounding it. The goal of this project is to determine optimal strategies for tiling your grid using techniques such as simulation to find optimal grid arrangements and clustering …

A System And Method For Measuring Spatially Varying Surface Appearances With A Study Of Feathers, Jessica Baron-Lis

All Dissertations

Real-world materials, particularly biological structures such as feathers exhibit complex appearances that vary spatially across their surfaces. The field of computer graphics provides a means of understanding such surfaces through material modeling which uses both analytical models and data acquired from light-surface interactions. There are many efforts within the past decade in measuring materials for graphics, but common limitations in these works include not accounting for spatially varying properties and reliance on neural networks and synthetic datasets.

Feathers from modern birds present diverse appearances due to how light interacts with their unique hierarchical microstructures. Variations in those structures lead to …

Mortgage Default Classification Modeling For Variable Analysis, Brendan R. Goggins

Honors College Theses

The financial crisis of the early 2000’s is a prime example of the severe consequences that mortgage default and borrower insolvency can have on economies at large. Mortgage default specifically is a prime case with the popularization of mortgage backed securities and the commonality of this loan structure. Multiple hypotheses and models have been formed to understand the reasons, causes, and consequences of mortgage default. This paper uses both machine learning and statistical classification models to inform an understanding of the variables most significant and impactful to the default outcome of mortgages. Consideration is given to both loan-level microeconomic variables …

An Analytical Prior Selection Procedure For Empirical Bayesian Analysis Using Resampling Techniques: A Simulation-Based Approach Using The Pancreatic Adenocarcinoma Data From The Seer Database, Aditya Chakraborty, Mohan D. Pant

Epidemiology, Biostatistics, & Environmental Health Faculty Publications

Introduction: In the field of medical research, empirical Bayesian analysis has emerged as an increasingly applicable approach. This statistical framework offers greater flexibility, enabling researchers to incorporate prior information and rigorously estimate parameters of interest. However, the selection of suitable prior distributions can be a challenging endeavor, with profound implications for the resulting inferences. To address this challenge, this study proposes a new analytical procedure that leverages resampling techniques to guide the choice of priors in Bayesian analysis. Subject and Methods: The study group consisted of patients who had been diagnosed and had died of pancreatic adenocarcinoma (cause-specific death) who …

Meditation In Qualitative Research For Bracketing And Beyond, Katalin Grajzel

Research Methods and Statistics: Graduate Student Scholarship

In this study, I recounted my experience using mantra meditation during a phenomenological study for the purposes of bracketing. The efficacy and purpose of bracketing have been debated from Husserl (1931), whose aimed was to achieve objectivity, to Heidegger (1962) who advocated for immersion of the researcher, through the French school (Merleau-Ponty, 1964) of middle ground, by whom bracketing was seen as the process to unearth and suspend biases for the better understanding of participants’ experiences (Arsel, 2017; Creswell & Creswell, 2017; Creswell & Poth, 2016; Fischer & Guzel, 2023). In this study, however, I propose another approach to bracketing …

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 …

Analysis Of Sled Dog Biomechanics, Natalie Bender

Williams Honors College, Honors Research Projects

This paper is an analysis of data collected by Dr Rachel Olson and her team. The data was collected from the same set of sled dogs before and after training for the Iditarod race. The goal of this paper is to draw conclusions on whether the gait of sled dogs’ change with fitness level. The data was cleaned in R to find the average peak for forelimb joint angles per run for each dog. The data was analyzed with 3 different ANOVAs – one including both the shoulder and carpus, one for just the shoulder, and one for just the …

Theoretical Foundations And Applied Performance Of Periodicity-Aware Imputation: Variable Bandpass Block Bootstrap Methods For Incomplete Time Series, Asmaa Ahmad

Electronic Theses & Dissertations (2024 - present)

Time series data are prevalent across a wide range of disciplines, including health surveillance, public policy, and environmental monitoring. In the presence of underlying cyclical patterns, the integrity of time series analysis depends critically on the ability to detect, model, and impute structured missing data without compromising the temporal structure. This dissertation introduces and validates a novel imputation framework that integrates the Variable Bandpass Periodic Block Bootstrap (VBPBB) into multiple imputation procedures, improving the accuracy, robustness, and interpretability of time series models under high rates of missingness and noise. The overarching goal of this dissertation was to develop and evaluate …