Statistics and Probability Commons^™

The Kumaraswamy Weibull Geometric Distribution With Applications, Mahdi Rasekhi, Morad Alizadeh, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this work, we study the kumaraswamy weibull geometric (Kw-WG) distribution which includes as special cases, several models such as the kumaraswamy weibull distribution, kumaraswamy exponential distribution, weibull geometric distribution, exponential geometric distribution, to name a few. This distribution was monotone and non-monotone hazard rate functions, which are useful in lifetime data analysis and reliability. We derive some basic properties of the Kw-WG distribution including non-central rth-moments, skewness, kurtosis, generating functions, mean deviations, mean residual life, entropy, order statistics and certain characterizations of our distribution. The method of maximum likelihood is used for estimating the model parameters and a simulation …

On Modified Burr Xii-Inverse Exponential Distribution: Prop¬Erties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Haitham M. Yousof, Azeem Ali, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution with increasing, increasing and decreasing and modified bathtub hazard rate called Modified Burr XII-Inverse Exponential (MBXII-IE) is introduced. The density function of MBXII-IE has exponential, left-skewed, right-skewed and symmetrical shapes. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The MBXII-IE distribution is characterized via different techniques. Parameters of MBXII-IE distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the Maximum Likelihood Estimates (MLEs) of the parameters of the MBXII-IE distribution. The …

A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks

Dissertations, Master's Theses and Master's Reports

To increase understanding of mercury cycling, a seasonal mass balance model was developed to predict mercury concentrations in lakes and fish. Results indicate that seasonality in mercury cycling is significant and is important for a northern latitude lake. Models, when validated, have the potential to be used as an alternative to measurements; models are relatively inexpensive and are not as time intensive. Previously published mercury models have neglected to perform a thorough validation. Model validation allows for regulators to be able to make more informed, confident decisions when using models in water quality management. It is critical to quantify uncertainty; …

Joint Analysis For Multiple Traits, Zhenchuan Wang

Dissertations, Master's Theses and Master's Reports

This dissertation includes three papers with each distributed in one chapter.

In chapter 1, we proposed an Adaptive Weighting Reverse Regression (AWRR) method to test association between multiple traits and rare variants in a genomic region. AWRR is robust to the directions of effects of causal variants and is also robust to the directions of association of traits. Using extensive simulation studies, we compared the performance of AWRR with canonical correlation analysis (CCA), Single-TOW, and the Weighted Sum Reverse Regression (WSRR). Our results showed that, in all of the simulation scenarios, AWRR is consistently more powerful than CCA. In most …

Algorithms For Reconstruction Of Gene Regulatory Networks From High -Throughput Gene Expression Data, Wenping Deng

Dissertations, Master's Theses and Master's Reports

Understanding gene interactions in complex living systems is one of the central tasks in system biology. With the availability of microarray and RNA-Seq technologies, a multitude of gene expression datasets has been generated towards novel biological knowledge discovery through statistical analysis and reconstruction of gene regulatory networks (GRN). Reconstruction of GRNs can reveal the interrelationships among genes and identify the hierarchies of genes and hubs in networks. The new algorithms I developed in this dissertation are specifically focused on the reconstruction of GRNs with increased accuracy from microarray and RNA-Seq high-throughput gene expression data sets.

The first algorithm (Chapter 2) …

An Efficient Method For Online Identification Of Steady State For Multivariate System, Honglun None Xu

Open Access Theses & Dissertations

Most of the existing steady state detection approaches are designed for univariate signals. For multivariate signals, the univariate approach is often applied to each process variable and the system is claimed to be steady once all signals are steady, which is computationally inefficient and also not accurate. The article proposes an efficient online method for multivariate steady state detection. It estimates the covariance matrices using two different approaches, namely, the mean-squared-deviation and mean-squared-successive-difference. To avoid the usage of a moving window, the process means and the two covariance matrices are calculated recursively through exponentially weighted moving average. A likelihood ratio …

On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models.

On Characterizations Of Mcllog, Ellogw, Pthl And K-Ge Distributions, Gholamhossein G. Hamedani, Nadeem Shafique Butt

Mathematics, Statistics and Computer Science Faculty Research and Publications

Huang S. and Oluyede (2016), Oluyede et al. (2016), Krishnarani (2016) and Rather and Rather (2017) consider the "McDonald Log-Logistic", the "Exponentiated Log-Logistic Weibull", the "Power Transformation Half-Logistic" and "k-Generalized Exponential" distributions, respectively, and study certain properties and applications of these distributions. The present short note is intended to complete, in some way, the above mentioned works via establishing certain characterizations of these distributions in different directions.

Characterizations And Infinite Divisibility Of Certain Recently Introduced Distributions Iii, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work may be a source of preventing reinventing and duplicating the existing distributions and calling them newly proposed distributions.

A Bayesian Variable Selection Approach Yields Improved Detection Of Brain Activation From Complex-Valued Fmri, Cheng-Han Yu, Raquel Prado, Hernando Ombao, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Voxel functional magnetic resonance imaging (fMRI) time courses are complex-valued signals giving rise to magnitude and phase data. Nevertheless, most studies use only the magnitude signals and thus discard half of the data that could potentially contain important information. Methods that make use of complex-valued fMRI (CV-fMRI) data have been shown to lead to superior power in detecting active voxels when compared to magnitude-only methods, particularly for small signal-to-noise ratios (SNRs). We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data. We develop models with complex-valued spike-and-slab priors on the activation …

Comparing Various Machine Learning Statistical Methods Using Variable Differentials To Predict College Basketball, Nicholas Bennett

Williams Honors College, Honors Research Projects

The purpose of this Senior Honors Project is to research, study, and demonstrate newfound knowledge of various machine learning statistical techniques that are not covered in the University of Akron’s statistics major curriculum. This report will be an overview of three machine-learning methods that were used to predict NCAA Basketball results, specifically, the March Madness tournament. The variables used for these methods, models, and tests will include numerous variables kept throughout the season for each team, along with a couple variables that are used by the selection committee when tournament teams are being picked. The end goal is to find …

Car Insurance Rate-Making With An Eye Toward The Future, Stephen Howard

Williams Honors College, Honors Research Projects

For my project, I investigated car insurance rate-making. I took an in-depth look at the car insurance industry. I also studied driverless cars, and the expected timeline surrounding them. I also took a look at how driverless cars are expected to change the car insurance industry in the coming decades. In general, what I found did not surprise me. I did, however, glean insight from various opinions that I read about how the insurance industry is likely to change. Change of some sort in the car insurance industry is sure to come, with companies likely to become much more multi-faceted. …

Matroid - Based Variable Selection For Complex Data Structures, Wimarsha Thathsarani Jayanetti

Open Access Theses & Dissertations

This research project has the objective to extend use of the matroid algorithm using statistically based criteria, Joint/Multivariate Cumulants (Speed, 1983) and Effective Dependence (Pena & Rodriguez, 2003) to capture linear as well as non-linear higher order dependencies. We also improve variable selection for complex data structures using the proposed matroid algorithm. The limiting distribution of the joint cumulant was defined using U-statistics theory by Hoeffding (1948). U-statistics variance as theorized by Hoeffding provide a lower bound for the estimated variance, and our simulation results justify the use of Hoeffding U-statistic variance for determining a threshold for joint cumulants deviation …

Using Data Mining To Model Student Achievement On The 4th Grade Timss 2015 Mathematics Assessment: A Five Nation Sudy, Annette M. Siemssen

Open Access Theses & Dissertations

Data mining has been successfully used by financial and retail companies since the mid-1960's to create predictive models and reveal unexpected relationships. However, it remains underutilized as a tool in educational research. Large-scale standardized assessment programs such as the Trends in International Mathematics and Science Study (TIMSS) provide vast amounts of data with the potential for providing new insights in education. Five nations, the Republic of Korea, the United States, Germany, Kuwait, and Kazakhstan were selected based on General Response Style theory to represent a spectrum of cultural backgrounds, from acquiescent to midpoint to individualistic (Hastedt, D. & van de …

Estimating The Optimal Cutoff Point For Logistic Regression, Zheng Zhang

Open Access Theses & Dissertations

Binary classification is one of the main themes of supervised learning. This research is concerned about determining the optimal cutoff point for the continuous-scaled outcomes (e.g., predicted probabilities) resulting from a classifier such as logistic regression. We make note of the fact that the cutoff point obtained from various methods is a statistic, which can be unstable with substantial variation. Nevertheless, due partly to complexity involved in estimating the cutpoint, there has been no formal study on the variance or standard error of the estimated cutoff point.

In this Thesis, a bootstrap aggregation method is put forward to estimate the …

Hierarchical Multiplicity Control Methods For Linear Models, Dimuthu Dilshan Fernando

Open Access Theses & Dissertations

HypoThesis testing is a commonly used statistical inference technique on which a statement of the population is investigated through the evidence from a representative sample of the population. With simultaneous testing of more than one null hypotheses need for an appropriate multiple comparison method is essential. With motivation from the study of Bogomolov et al. (2017) we have modified a multiple comparison tree structure to build the required comparisons and focus on controlling the FWER (Family Wise Error Rate) using the Bonferroni procedure. The proposed method has advantages such as controlling the global error rates separately at each level, families …

Backward Elimination Algorithm For High Dimensional Variable Screening, Sophia Korkor Foli

Open Access Theses & Dissertations

In recent times, variable selection in high-dimensional data has become a challenging prob- lem. We investigate here a popular but classical variable screening method, the Back- ward Elimination (BE) in a high dimensional setup (small-n-large P). The BE method as a variable screening method reduces the dimension of small-n-large P data into a lower dimensional data and then established shrinkage methods such as: LASSO, SCAD and MCP can be applied directly. To overcome the problems in high dimensional data, Chen and Chen (2008) recently developed a family of Extended Bayesian Information Criterion (EBIC) which is consistent with finite sample properties …

Extraction Of Fiber Morphology From Sem Images For Quality Control Of Fiber Reinforced Composites Manufacturing, Md Fashiar Rahman

Open Access Theses & Dissertations

The morphology of fibers (e.g. spatial uniformity, orientation, and length) plays a decisive role in determining the material properties or fabrication quality of fiber-reinforced nanocomposites. Hence, determining the morphology becomes a very critical issue in the field of nanocomposite quality control. The conventional way of quality inspection is to take the scanning electron microscopic (SEM) images of the cross-section of composite material and do the visual checking of these SEM images to evaluate the nanofiber alignment and length distribution. But this type of inspection is often subjective, inaccurate and time consuming. Moreover, the extremely small size of nanofibers makes the …

Impact Of Highway Work Zones On Traffic Crashes: A Case Study In Michigan, Qadri Hafez Shaheen

Master's Theses and Doctoral Dissertations

Infrastructure in the US is severely aged and outdated. This presents a seemingly paradoxical problem in the field of construction management: In order to fix and make roads and highways more safe, construction zones must become inherently less safe in the process. There is a high cost to taxpayers and drivers, as work zones experience a significant amount of crashes and fatalities each year. To mitigate some of the factors that contribute to these crashes, this paper attempts to deliver guidelines on how to update relevant crash data, identify relevant factors, and create recommendations accordingly. The research focused particularly on …

Forensic Detection For Earnings Management In Selected Code Law Nations Of Europe, Jef Lee Garner

Walden Dissertations and Doctoral Studies

This study investigated earnings management in European firms. The private investors became victims of manipulated earnings where few laws offered regulatory oversight. The study forensically examined the attributes of earnings management identified using a discretionary accrual model published in Jones' work and Schippers' work. The firms' managers should fulfil agency theory when they made reporting decisions, and they should act in the investors' best interests to fulfil stewardship theory. The managers failed as they seemed to favor insiders when they reported manipulated earnings to outsiders like small investors even though the managers published financial reports conforming to the International Financial …