Statistics and Probability Commons^™

Exact X2 Statistic Critical Values For Dice Fairness Testing, Warren Campbell

SEAS Faculty Publications

Two questions were addressed: 1) What are the exact values of the c² statistic critical values? 2. Does a dice tower offer improved fairness of dice rolls?  Critical values of the statistic asymptotically approach those given by the continuous chi-square distribution, but the exact distribution is discrete.  The exact distributions only asymptotically approach the chi-square distribution, and the convergence is slow (1/number of rolls).  Th exact distributions are a function of the number of rolls, the chi-square distribution is not a function of the number of rolls.  Exact values of c² at the 90, 95, and 99 percent …

Correlation Visualizer, Manish Rami

Software

An interactive tool to understand correlations. The tool uses an example relationship between phonological awareness (CTOPP-2) and reading fluency. Both measures use standard scores (M = 100, SD = 15). Viewers can adjust r to explore how the strength and direction of correlation affects the scatter pattern and shared variance. Use the slider for r to see corresponding changes in the plot and the values of r and effect size.

It's All In The (Exponential) Family: An Equivalence Between Maximum Likelihood Estimation And Control Variates For Sketching Algorithms, Keegan Kang, Kerong Wang, Ding Zhang, Rameshwar Pratap, Bhisham Dev Verma, Benedict Wong

Faculty Conference Papers and Presentations

Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an exponential family, an optimal CVE will achieve the same asymptotic variance as the MLE, giving a fixed point algorithm for the MLE. Experiments show the fixed point algorithm is faster and numerically stable compared to other root finding algorithms for the MLE for the bivariate Normal distribution, and we expect this to hold across distributions satisfying these conditions. We show how this algorithm leads to reproducibility for …

What We Know About Accounting Ratios: Methodological Considerations, Wojciech Kuryłek, Oskar Kowalewski

Studia i Materiały Wydział Zarządzania Uniwersytet Warszawski

Purpose: This paper provides a comprehensive literature review of the methodological aspects of financial ratio analysis, consolidating dispersed knowledge on the computation, statistical properties, and appropriate usage of accounting ratios.

Design/Methodology/Approach: The study adopts a narrative literature review methodology, systematically surveying published research on financial ratio distributions, normality testing, data transformations, outlier handling, the proportionality assumption, dimensionality reduction techniques, compositional data analysis, and recommended ratio sets for corporate financial research.

Findings: Financial ratios predominantly deviate from normal distributions, exhibiting skewness, excess kurtosis, and sensitivity to outliers. Transformation techniques such as logarithmic, square root, and Box‑Cox methods yield mixed results in …

Interactive Distribution Visualizer, Manish Rami

Software

An interactive tool visualizing types of distribution. Viewers can morph between a bell curve, box plot, and cumulative frequency curve.

Reliability Vs. Validity Visualizer, Manish Rami

Software

A visualization tool to demonstrate the concepts of reliability and validity.

Each target represents repeated measurements of the same person or construct. The crosshair (✛) marks the true score. Reliability = how tightly shots cluster together. Validity = whether shots center on the true score. Click any panel for a clinical SLP example. Also see notes below the plots.

Mengukur Capaian Dan Identifikasi Konvergensi Pembangunan Infrastruktur Antarprovinsi Di Indonesia, Ressa Isnaini Arumnisaa', Aisyah Fitri Yuniasih

Jurnal Ekonomi dan Pembangunan Indonesia

Indonesia’s economic challenges are characterized by stagnant economic growth and regional development disparities. This study analyzes the achievement and convergence of infrastructure development across provinces in Indonesia during 2011–2021 through the construction of an Infrastructure Development Index (IPI). The study employs panel data from 33 provinces, using factor analysis to construct the IPI and the First Difference Generalized Method of Moments (FD-GMM) to examine convergence and its determinants. The results show that many provinces still have IDI scores below the national average. Furthermore, the FD-GMM model shows that σ-convergence and β-convergence occur in Indonesia. In addition, GRDP per capita, inflation, …

Estimasi Underground Economy Triwulanan Di Indonesia Pada Tahun 2010–2023, Ghina Anandhia, Hardius Usman

Jurnal Ekonomi dan Pembangunan Indonesia

Underground economics have a significant impact on economy. Underground economy leads to low potential state revenues from the tax sector. This study estimates the quarterly value of the underground economy in Indonesia from 2010 to 2023 using the Error Correction Model (ECM) method. The results show that the average value of the underground economy in Indonesia is IDR138,392.32 billion, equivalent to 5.36 percent of Gross Domestic Product (GDP) and 35.72 percent of tax revenue from 2010 to 2023. GDP and tax burden variables have a positive influence on currency demand.

Item Response Theory Evaluation Of Mental Health Sentiment Scales, Muhammad Amzad Hossain

Graduate Theses and Dissertations

Mental health is an essential part of overall well-being. Accurate measurement of constructs such as loneliness, anxiety, depression, and life satisfaction is extremely important in research and practice. Traditional approaches based on Classical Test Theory (CTT) are limited. They rely on total test scores and assume constant measurement error across individuals. They may not reflect true variability in measurement precision (Zein & Akhtar, 2025; Marvianto, 2023). In contrast, Item Response Theory (IRT) provides an advanced approach by examining item-level performance. It models the relationship between latent traits and responses (Zein & Akhtar, 2025 ). To address these limitations, this study …

Univariate And Bivariate Binary Spatial Regression Models With Application To Plant Abundance Data, Amir Hamza Akash

Graduate Theses and Dissertations

Analyzing species distributions is of prime interest in ecological research. Prevalence of a species usually depends on several environmental and topographic features not all of which can be quantified or measured. Spatial random effects play an important role as a surrogate for missing features that can explain similarity in species prevalence patterns between neighboring locations. In this thesis, we focus on a dataset on abundance of plants in the southern part of South Africa. First, we build a hierarchical Bayesian model for binary regression, using the probit link, on presence/ absence of a species based on available covariates. Since the …

Statistical Machine Learning For Calibrating Climate Model Wind Fields., Augustine Ouru

Graduate Theses and Dissertations

This thesis investigates statistical calibration methods for wind data from Global Climate Models (GCMs), with emphasis on wind speed and wind direction. The analysis uses 30 years of daily observed and GCM wind records from 9 spatial locations in the South East USA. Wind is represented in polar coordinates, but also often modeled in Cartesian coordinates. Four calibration models are compared: a marginal wind speed model, an independent Cartesian model. The calibration models are based on semi-parametric quantile regression, a flexible conditional density estimator fitted using neural networks. The neural network objective functions are optimized using maximum likelihood estimation (MLE) …

Statistical Evaluation Of A New Orleans Historic Rainfall Dataset (1840–1893), Arielle C. Filostrat

LSU Master's Theses

This study evaluates the climatic credibility of a newly identified historical rainfall dataset for New Orleans, Louisiana, spanning 1840–1893. The New Orleans Historical Dataset (NOHD) is compared to a modern observational record from the Audubon rain gauge (1893–2024) to determine whether nineteenth-century rainfall observations are consistent with known precipitation behavior in the region. Establishing the reliability of early records is critical for extending climatological baselines and improving understanding of long-term rainfall variability.

Historical rainfall observations were first evaluated through archival review using the New Orleans Medical and Surgical Journal and other nineteenth-century meteorological records to verify notable rainfall events. Daily …

Stochastic Analysis Of Epidemic Size And Peak Infection In An Svir Model With Imperfect Vaccine And External Source Of Infection, María Gamboa Pérez

Mathematical Modelling and Numerical Simulation with Applications

The dynamics of an infectious disease outbreak are studied under a stochastic framework in a closed population where individuals are homogeneously mixed. A vaccination program is implemented in the community prior to the start of the epidemic. The administered vaccine is imperfect, meaning that vaccinated individuals may still become infected upon contact with infected individuals. The mathematical Susceptible-Vaccinated-Infected-Recovered (SVIR) model describing the evolution of the epidemic is formulated as an absorbing, continuous-time, three-dimensional Markov chain with compartments for vaccinated, susceptible, infected and recovered individuals. The aim of this study is to characterize two fundamental epidemiological quantities: the maximum number of …

Study On Deformation Characteristics Of Kaolin Under Dry-Wet And Freeze-Thaw Cycles, Yang Shang, Xiao Dingyuan

Journal of China & Foreign Highway

In seasonally frozen areas, surface soil is subjected to prolonged and drastic fluctuations in temperature and humidity, causing excessive deformation and resulting in engineering issues such as subgrade settlement and building deformation. The deformation characteristics of kaolin in seasonally frozen areas under the combined influence of freeze-thaw and dry-wet cycles were studied. Through a self-designed experimental setup, experiments with interleaved dry-wet and freeze-thaw cycles were conducted on compacted specimens, and wetting-freezing-thawing-drying cycle experiments were performed to explore the swelling-shrinkage deformation characteristics of kaolin under the combined action of different freeze-thaw and dry-wet cycles. The results indicate that intermittent freeze-thaw cycles …

Material Point Method Simulation Of Soil Landslide Considering Interface Friction Effect, Zuo Zhipeng, Hu Shengliang, Li Maowen, Tong Chenxi, Li Haichao

Journal of China & Foreign Highway

During the high-speed and long-runout sliding failure process of large landslides, severe friction and heat generation in the sliding zone induce an interface friction effect between the debris flow and the bedrock, influencing the final accumulation morphology of the landslide. In this paper, a two-dimensional landslide model of the Yangbaodi landslide in Shenzhen was established using the material point method. A contact algorithm was introduced through a multi-background grid method to conduct numerical simulations on the initiation, sliding, and accumulation processes of the landslide. The results show that after initiation, the landslide moves over a long distance in a flow-like …

Influence Of Geocell Technical Parameters On Bearing Characteristics Of Highway Subgrades In Oasis Areas, Zhu Chunsheng, Shu Xingyu, Lu Huiyu, Yang Xiaohua

Journal of China & Foreign Highway

To study the effects of technical parameters, such as geocell specifications and laying types, on the bearing capacity and deformation of highway subgrades in oasis flood irrigation areas, the shear properties of plain soil and geocell-reinforced layers with different specifications were studied through large-scale direct shear tests. Based on indoor compression tests and field load tests, numerical simulation parameters, such as the deformation modulus of different foundation soil layers, were calibrated. A numerical model of the geocell-reinforced highway subgrade was established using, and the effects of geocell specifications and laying types on the vertical settlement of the subgrade, the displacement …

Stratified Multi-Well Pumping Tests And Back-Analysis Of Hydraulic Conductivity In Ultra-Deep Circular Foundation Pits, Luo Renkun, Wang Jie

Journal of China & Foreign Highway

Dewatering prior to foundation pit excavation is a critical measure to prevent engineering hazards such as slope instability at the pit top, seepage around the pit, and bottom heave. As a key parameter in dewatering design, hydraulic conductivity directly influences the risk control in foundation pit engineering. Based on the east anchor foundation pit project of the Shiziyang Passageway, single-well pumping tests and stratified multi-well pumping tests were conducted. The water level variations in the internal dewatering wells and the external observation wells were monitored in stages. Accordingly, a finite difference numerical model for the pumping tests was established. The …

Study On Effects Of Phase Change Materials On Thermal Erosion Resistance Of Airport Pavement, Li Ping, Li Yunlong, Zheng Zhipeng, Wang Zhijian, Yi Chengxi

Journal of China & Foreign Highway

To investigate the effect of phase change materials (PCMs ) on improving the thermal erosion resistance of airport pavements and to provide recommendations for selecting optimal PCMs to obtain airport pavements with longer service lives, three PCMs, PCM-G- 98 (A), LB- 2 (B), and TH-HC- 120 (C), were purchased based on literature summaries and market research. Based on microscopic test results and the actual preparation conditions of modified asphalt, PCMs A and B were selected. Subsequently, based on a self-made high-content SBS modified asphalt (S), four groups of composite modified asphalts (S-A- 5, S-A- 10, S-B- 5, and S-B- 10) …

Research On Mechanical Properties And Particle Breakage Of Construction Solid Waste Concrete Under Cyclic Loading, Li Xuejian, Song Yang, Dong Chenxi, Li Shengkai, Li Wangyuan

Journal of China & Foreign Highway

To investigate the mechanical properties and particle breakage effect of construction solid waste, a series of static and dynamic direct shear tests were carried out using a dynamic interface shear tester. Different coarse particle contents (40%, 50%, and 60%), amplitudes (45 kPa, 60 kPa, and 75 kPa), and frequencies (0.5 Hz, 1 Hz, and 2 Hz) were used as variables, and the variation rules of shear stress‒shear displacement curves, shear strength parameters, and particle breakage under three normal stresses (50 kPa, 100 kPa, and 150 kPa) were analyzed. The results indicate that under the same initial normal stress, with the …

Study On Influence Of Elastic Modulus Of Fiber On Compaction Characteristics Of Asphalt Mixtures, Zou Zexi, Luo Kaiyan, Lin Zhiming, Qiu Xiang, Lu Xudong, Yao Xiaoyang, Wang Yaolong

Journal of China & Foreign Highway

To investigate the influence mechanism of fiber incorporation on the compaction characteristics of asphalt mixtures, six types of typical road fibers (polyester fiber, polyacrylonitrile fiber, aramid fiber, basalt fiber, polypropylene fiber, and polyvinyl alcohol fiber) were selected in this paper, and gyratory compaction tests were conducted based on AC- 20 graded mixtures. The compaction coefficient (a larger compaction coefficient indicates easier compaction) was used as the core evaluation index. The results indicate that the elastic modulus of the fiber is the key influencing factor. When the fiber modulus is 50% lower than the aggregate modulus (such as polyester fiber and …