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 …

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.

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 …

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.

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 …

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 …

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) …

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 …

Angularity Evaluation Of Coarse Aggregates Based On Local Feature Extraction Of Point Clouds, Ma Quanzhuo, Feng Ponan, Feng Zezhong, Lei Mingyu, Wang Zhenfeng, Li Jiange

Journal of China & Foreign Highway

The morphological characteristics of coarse aggregates significantly affect the mechanical properties of asphalt mixtures and thus directly influence their road performance and durability. This paper aims to innovatively propose an evaluation method for the angularity of coarse aggregates. A three-dimensional (3D) scanner was used to acquire the surface profile information of coarse aggregates, and local angularity features were extracted through point cloud data analysis. Subsequently, a comprehensive 3D angularity evaluation index for coarse aggregates (A3D) was proposed by combining local normal vectors and curvature characteristics. The results indicate that A3D can be more accurately and independently used for angularity evaluation. …

Optimization Design And Experimental Study On Strength Of Ternary Industrial Solid Waste Mixtures, Yang Shu, Ai Yi, Sheng Shanwang, Li Chuangmin

Journal of China & Foreign Highway

This paper aims to explore whether fly ash, lithium slag, and slag powder (ternary industrial solid wastes) can effectively replace cement as cementitious materials for interlocking large-particle crushed stone bases. A uniform design table U9(94) was used to design the test scheme for the mixing ratios of ternary industrial solid waste mixtures; the correlation between the mortar strength and the ternary industrial solid waste mixtures was analyzed by Pearson correlation; with the help of the mathematical statistical software SPSS 26.0, mathematical models for the flexural strength and compressive strength of the ternary industrial solid waste mixture mortar specimens were established. …

Calculation Of Tensile Force For Cable-Stayed Buckling Bracket Combined With Temporary Tie Rod Structure Of V-Shaped Pier, Zhao Xiaolu, Yang Guang, Liu Junle, Qiu Zhiwei, Meng Lingxin, Peng Weibing

Journal of China & Foreign Highway

To solve the problem of excessive tensile stress of the cross-section during the cantilever casting process of high piers with inclined legs, a determination method of tensile force based on the linear programming theory and unstressed state control was proposed. Based on the internal force equilibrium method and the principle of influence matrix, the method optimized the tensile force with “stress control as the primary and alignment control as the auxiliary”. The unstressed state control method was adopted for forward iteration, and the effect of tangential displacement between segments was considered to verify the alignment of the inclined legs. Finally, …

Analysis Of Influence Of Cable Clamp Slippage On Internal Force And Alignment Of Main Cable, Zhu Kun, Liao Dinghui, Hu Chengze, Shen Heshun, Cao Hongyou

Journal of China & Foreign Highway

To investigate the influence of cable clamp slippage on alignment and internal force of the main cable, a theoretical analysis method based on node coordinates of the main cable after cable clamp slippage was proposed in this paper. Based on segmented catenary theory, the influence of hanger inclination caused by hanger slippage on the horizontal force of the main cable was considered. The segmental cable element of the main cable was equivalently expressed as expressions of hanger tension and unstressed length. With total unstressed length kept constant as a control condition, the horizontal force of the main cable was iteratively …

Study On Structural Design And Load Transfer Performance Of 6-Hole Flat Anchor Plate, Liao Yuanyuan, Ling Lihua, Wu Qibin, Cheng Bin, Dai Dongming

Journal of China & Foreign Highway

For negative bending moment prestressed tendons in simply supported-to-structurally-continuous bridges, the flat anchorage method of flange plate is more reasonable, but its widespread application is limited due to the anchoring capacity restrictions of flat anchor plates. To improve the anchoring capacity of a single anchorage zone, reduce the number of prestressed ducts, save concrete, and improve construction efficiency, a novel 6-hole flat anchor plate was developed, designed, and manufactured in this paper. By combining finite element analysis and experimental methods, a finite element analysis model of the concrete load transfer specimen beneath the novel 6-hole flat anchor plate was established, …

Analysis Of Shear Bearing Mechanism And Influencing Factors Of Mcl-Shaped Composite Dowel Connector, Zeng Zhuo, Zhou Baicheng, Cheng Xianjie, Cao Zhengxing, Gao Rongxiong, Wang Zichao

Journal of China & Foreign Highway

To investigate the bearing mechanism of modified clothoid (MCL)-shaped composite dowel shear connectors and the influence laws of various factors on their shear bearing capacity, the stress states and failure modes of the steel dowel, concrete dowel, and transverse through-reinforcement that constitute the MCL-shaped shear connector were deeply analyzed in this paper based on an experimentally validated finite element model. Furthermore, the influence laws of transverse through-reinforcement, steel dowel thickness, and concrete strength on the shear bearing capacity of the MCL-shaped composite dowel were explored. The research results indicate that the bearing process of the MCL-shaped composite dowel exhibits elastic, …

Research On Improving Bearing Capacity Of Full-Scale Prestressed Concrete Small Box Girders, Huang Jianyun, Gao Linli, Liu Zufeng, Ma Jinku, Ma Ming, Wang Xiaoguang

Journal of China & Foreign Highway

To solve the problems of lacking comparative research on the improvement effects of different reinforcement methods when formulating reinforcement schemes for prestressed concrete small box girders and that existing bearing capacity improvement tests mostly focus on scale models with insufficient reliability of results, full-scale model tests and numerical simulation analysis of five 30 m span prestressed concrete small box girders with different joint reinforcement measures were conducted in this paper. Finite element models for two single reinforcement measures were established, and the improvement effects of different reinforcement methods on the bearing capacity of prestressed concrete small box girders were studied. …