Statistics and Probability Commons^™

An Examination Of Computational Methods Related To G/M/C Queueing, Thomas Michaud Ms

All Student Scholarship

The following examination of computational methods related to queues with general arrivals (i:i:d: but of unknown distribution), multiple identical servers with i:i:d: exponential service times, and ordinary first come, first served service (hereafter referred to as G/M/c to use existing naming conventions) seeks to investigate the current models and provide new results based on a draft convolution method proposed by El-Taha[3]. The new model will demonstrate the use of distributions with coefficients of variance ranging from zero to near infinity to provide flexibility in simulating a range of potential arrival distributions, and we include detailed results and software for both …

A Self-Contained Course In The Mathematical Theory Of Statistics For Scientists & Engineers With An Emphasis On Predictive Regression Modeling & Financial Applications., Tim Smith

Open Access Textbooks

Preface & Acknowledgments

This textbook is designed for a higher level undergraduate, perhaps even first year graduate, course for engineering or science students who are interested to gain knowledge of using data analysis to make predictive models. While there is no statistical perquisite knowledge required to read this book, due to the fact that the study is designed for the reader to truly understand the underlying theory rather than just learn how to read computer output, it would be best read with some familiarity of elementary statistics. The book is self-contained and the only true perquisite knowledge is a solid …

The Use Of 3-D Highway Differential Geometry In Crash Prediction Modeling, Kiriakos Amiridis

Theses and Dissertations--Civil Engineering

The objective of this research is to evaluate and introduce a new methodology regarding rural highway safety. Current practices rely on crash prediction models that utilize specific explanatory variables, whereas the depository of knowledge for past research is the Highway Safety Manual (HSM). Most of the prediction models in the HSM identify the effect of individual geometric elements on crash occurrence and consider their combination in a multiplicative manner, where each effect is multiplied with others to determine their combined influence. The concepts of 3-dimesnional (3-D) representation of the roadway surface have also been explored in the past aiming to …

Fixed Choice Design And Augmented Fixed Choice Design For Network Data With Missing Observations, Miles Q. Ott, Matthew T. Harrison, Krista J. Gile, Nancy P. Barnett, Joseph W. Hogan

Statistical and Data Sciences: Faculty Publications

The statistical analysis of social networks is increasingly used to understand social processes and patterns. The association between social relationships and individual behaviors is of particular interest to sociologists, psychologists, and public health researchers. Several recent network studies make use of the fixed choice design (FCD), which induces missing edges in the network data. Because of the complex dependence structure inherent in networks, missing data can pose very difficult problems for valid statistical inference. In this article, we introduce novel methods for accounting for the FCD censoring and introduce a new survey design, which we call the augmented fixed choice …

Cramer Type Moderate Deviations For Random Fields And Mutual Information Estimation For Mixed-Pair Random Variables, Aleksandr Beknazaryan

Electronic Theses and Dissertations

In this dissertation we first study Cramer type moderate deviation for partial sums of random fields by applying the conjugate method. In 1938 Cramer published his results on large deviations of sums of i.i.d. random variables after which a lot of research has been done on establishing Cramer type moderate and large deviation theorems for different types of random variables and for various statistics. In particular results have been obtained for independent non-identically distributed random variables for the sum of independent random to estimate the mutual information between two random variables. The estimates enjoy a central limit theorem under some …

Development Of A Data-Driven Patient Engagement Score Using Finite Mixture Models, Eric Bae

Electronic Theses and Dissertations

Patient activation measure (PAM) is widely adopted by health care providers to access individual's knowledge, skill, and confidence for managing one's health and healthcare. Patient activation measure (PAM), licensed by Insignia Health, is widely adopted by health care providers to access individual's knowledge, skill, and confidence for managing one's health and healthcare. Multiple studies corroborate the effectiveness of activation measure in predicting most health behaviors, including preventive behaviors, healthy behaviors, self-management behaviors, and health information seeking. However, PAM is heavily dependent on subjective patient-reported data, which are often incomplete. The purpose of this study is to develop an objective statistical …

Quasilinearization And Boundary Value Problems At Resonance For Caputo Fractional Differential Equations, Saleh S. Almuthaybiri, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

The quasilinearization method is applied to a boundary value problem at resonance for a Caputo fractional differential equation. The method of upper and lower solutions is first employed to obtain the uniqueness of solutions of the boundary value problem at resonance. The shift argument is applied to show the existence of solutions. The quasilinearization algorithm is then developed and sequences of approximate solutions are constructed that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two applications are provided to illustrate the main results.

Modeling Stochastically Intransitive Relationships In Paired Comparison Data, Ryan Patrick Alexander Mcshane

Statistical Science Theses and Dissertations

If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could Spurs fans make a legitimate argument that their team is better despite this chain of evidence?

We first explore the nature of intransitive (rock-scissors-paper) relationships with a graph theoretic approach to the method of paired comparisons framework popularized by Kendall and Smith (1940). Then, we focus on the setting where all pairs of items, teams, players, or objects have been compared to …

The Impact Of College Athletic Success On Donations And Applicant Quality, Benjamin Baumer, Andrew Zimbalist

Mathematics Sciences: Faculty Publications

For the 65 colleges and universities that participate in the Power Five athletic conferences (Pac 12, Big 10, SEC, ACC, and Big 12), the football and men’s basketball teams are highly visible. While these programs generate tens of millions of dollars in revenue annually, very few of them turn an operating “profit.” Their existence is thus justified by the claim that athletic success leads to ancillary benefits for the academic institution, in terms of both quantity (e.g., more applications, donations, and state funding) and quality (e.g., stronger applicants, lower acceptance rates, higher yields). Previous studies provide only weak support for …

Improving Access To Clean Water In Rural Ecuador: The Connection Between Willingness To Pay And Population Health, Micalea Leaska

Capstone Collection

Climate change is affecting social and environmental determinants of health through access to safe drinking water, safely managed sanitation systems, and access to health care services and the ability for individuals to break free from unsuitable circumstances. Ecological disturbances such as those caused by climate change can cause a shift in host vectors or a change in habitat that results in a greater likelihood of the pathogen coming in contact with humans. Water, sanitation, and hygiene (WASH) services and their accessibility to populations can directly impact a community’s vulnerability to diseases and limiting factors to increase economic growth. If rural …

The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul W. Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul

Mathematics Faculty Publications

In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation. (See paper for equation.)

We employ a Krasnosel’skii type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified.

Characterizations Of Certain Recently Introduced Discrete Distributions, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of certain recently introduced discrete distributions are presented to complete, in some way, the works cited in the References.

Cronbach’S Alpha Under Insufficient Effort Responding: An Analytic Approach, Stephen W. Carden, Trevor R. Camper, Nicholas S. Holtzman

Psychology: Faculty Publications

Surveys commonly suffer from insufficient effort responding (IER). If not accounted for, IER can cause biases and lead to false conclusions. In particular, Cronbach’s alpha has been empirically observed to either deflate or inflate due to IER. This paper will elucidate how IER impacts Cronbach’s alpha in a variety of situations. Previous results concerning internal consistency under mixture models are extended to obtain a characterization of Cronbach’s alpha in terms of item validities, average variances, and average covariances. The characterization is then applied to contaminating distributions representing various types of IER. The discussion will provide commentary on previous simulation-based investigations, …

Neutrosophic Set Is A Generalization Of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set, Q-Rung Orthopair Fuzzy Set, Spherical Fuzzy Set, And N-Hyperspherical Fuzzy Set, While Neutrosophication Is A Generalization Of Regret Theory, Grey System Theory, And Three-Ways Decision (Revisited), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IFS) no matter if the sum of single-valued neutrosophic components is < 1, or > 1, or = 1. For the case when the sum of components is 1 (as in IFS), after applying the neutrosophic aggregation operators one gets a different result from that of applying the intuitionistic fuzzy operators, since the intuitionistic fuzzy operators ignore the indeterminacy, while the neutrosophic aggregation operators take into consideration the indeterminacy at the same level as truth-membership and falsehood-nonmembership are taken. NS is also more flexible and effective because it …

Robust Statistical Inference For The Gaussian Distribution, Andrews Tawiah Anum

Open Access Theses & Dissertations

The aim of robust statistics is to develop statistical procedures which are not unduly influenced by outliers or observations that are not representative of the underlying "true" data generating process. This thesis focuses on an estimator with this characteristic. The divergence function is introduced in Chapter 2 with the sole aim of taking the function f to be the univariate normal distribution and α - [0, 1]. The estimator fails when we rely on the classic Newton's method to converge to the minimum of the density power divergence (MDPD) function. There is a tendency of such estimator never to approach …

Forecasting Crashes, Credit Card Default, And Imputation Analysis On Missing Values By The Use Of Neural Networks, Jazmin Quezada

Open Access Theses & Dissertations

A neural network is a system of hardware and/or software patterned after the operation of neurons in the human brain. Neural networks,- also called Artificial Neural Networks - are a variety of deep learning technology, which also falls under the umbrella of artificial intelligence, or AI. Recent studies shows that Artificial Neural Network has the highest coefficient of determination (i.e. measure to assess how well a model explains and predicts future outcomes.) in comparison to the K-nearest neighbor classifiers, logistic regression, discriminant analysis, naive Bayesian classifier, and classification trees. In this work, the theoretical description of the neural network methodology …

The Exponentiated Generalized Topp Leone-G Family Of Distributions: Properties And Applications, Hesham Mohammed Reyad, Morad Alizadeh, Farrukh Jamal, Soha Othman, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we propose a new class of continuous distributions called the exponentiated generalized Topp Leone-G family that extends the Topp Leone-G family introduced by Al-Shomrani et al. (2016). We derive explicit expressions for certain mathematical properties of the new family such as; ordinary and incomplete moments, generating functions, reliability analysis, Lorenz and Bonferroni curves, Rényi entropy, stress strength model, moment of residual and reversed residual life, order statistics, extreme values and characterizations. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the flexibility of …

The Nested Joint Clustering Via Dirichlet Process Mixture Model, Shengtong Han, Hongmei Zhang, Wenhui Sheng, Hasan Arshad

Mathematical and Statistical Science Faculty Research and Publications

This article focuses on the clustering problem based on Dirichlet process (DP) mixtures. To model both time invariant and temporal patterns, different from other existing clustering methods, the proposed semi-parametric model is flexible in that both the common and unique patterns are taken into account simultaneously. Furthermore, by jointly clustering subjects and the associated variables, the intrinsic complex shared patterns among subjects and among variables are expected to be captured. The number of clusters and cluster assignments are directly inferred with the use of DP. Simulation studies illustrate the effectiveness of the proposed method. An application to wheal size data …

Cubic Rank Transmuted Modified Burr Iii Pareto Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Wenhui Sheng, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. …

On Burr Iii Marshal Olkin Family: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Gauss M. Cordeiro, Haitham M. Yousof, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the …

On Burr Iii-Pareto Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a new four parameter lifetime model with increasing, decreasing, increasing-decreasing, decreasing-increasing-decreasing, modified bathtub, bathtub and inverted bathtub hazard rate function called Burr III-Pareto (BIII-Pareto) is developed on the basis of the T-X family technique. The BIII-Pareto density function is arc, J-shape, reverse J-shape, positively, negatively skewed and symmetrical. Some structural and mathematical properties including moments, moments of order statistics, inequality measures and reliability measures are theoretically established. The BIII-Pareto distribution is characterized via different techniques. Parameters of the BIII-Pareto distribution are estimated using maximum likelihood method. The simulation study for performance of the maximum likelihood estimates (MLEs) …

On The Modified Burr Xii-Power Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution with increasing, decreasing and bathtub hazard rate called the Modified Burr XII-Power (MBXII-Power) is developed on the basis of the T-X family technique. The density function of the MBXII-Power is arc, exponential, left-skewed, right-skewed, J, reverse-J and symmetrical shaped. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBXII-Power distribution is characterized via different techniques. Parameters of the MBXII-Power distribution are estimated using maximum likelihood method. The simulation study is performed on the basis of graphical results to see …

Does It Take Three To Dance The Tango? Organizational Design, Triadic Structures And Boundary Spanning Across Subunits, Stefano Tasselli, Alberto Caimo

Articles

In this paper, we investigate the processes of boundary spanning across subunits within organizational networks. We hypothesize that patterns of advice across organizational subunits are explained by different triadic mechanisms depending on the organizational design of the intra-organizational network. In organizational networks characterized by flat hierarchy, we found triadic cyclic closure to be positively associated to boundary spanning across subunits; but when the network reflects an organizational structure with formal hierarchical differentiation among members, then we found triadic transitive closure to be associated to boundary spanning across subunits. We test these predictions in two empirical studies consisting of two organizational …

On The Generalized Log Burr Iii Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Azeem Ali, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we present a generalized log Burr III (GLBIII) distribution developed on the basis of a generalized log Pearson differential equation (GLPE). The density function of the GLBIII is exponential, arc, J, reverse-J, bimodal, left-skewed, right- skewed and symmetrical shaped. The hazard rate function of GLBIII distribution has various shapes such as constant, increasing, decreasing, increasing-decreasing, upside- down bathtub and modified bathtub. Descriptive measures such as quantile function, sub- models, ordinary moments, moments of order statistics, incomplete moments, reliability and uncertainty measures are theoretically established. The GLBIII distribution is characterized via different techniques. Parameters of the GLBIII distribution …

A New Extension Of Lindley Distribution: Modified Validation Test, Characterizations And Different Methods Of Estimation, Mohamed Ibrahim, Abhimanyu Singh Yadav, Haitham M. Yousof, Hafida Goual, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. …

Nonparametric Collective Spectral Density Estimation With An Application To Clustering The Brain Signals, Mehdi Maadooliat, Ying Sun, Tianbo Chen

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log‐SDF can be represented using a common set of basis functions. The basis shared by the collection of the log‐SDFs is estimated as a low‐dimensional manifold of a large space spanned by a prespecified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Moreover, each estimated spectral density has a concise representation using the …

Power In Pairs: Assessing The Statistical Value Of Paired Samples In Tests For Differential Expression, John R. Stevens, Jennifer S. Herrick, Roger K. Wolff, Martha L. Slattery

Mathematics and Statistics Faculty Publications

Background: When genomics researchers design a high-throughput study to test for differential expression, some biological systems and research questions provide opportunities to use paired samples from subjects, and researchers can plan for a certain proportion of subjects to have paired samples. We consider the effect of this paired samples proportion on the statistical power of the study, using characteristics of both count (RNA-Seq) and continuous (microarray) expression data from a colorectal cancer study.

Results: We demonstrate that a higher proportion of subjects with paired samples yields higher statistical power, for various total numbers of samples, and for various strengths of …

Almost Periodic Functions In Quantum Calculus, Martin Bohner, Jaqueline Godoy Mesquita

Mathematics and Statistics Faculty Research & Creative Works

In this article, we introduce the concepts of Bochner and Bohr almost periodic functions in quantum calculus and show that both concepts are equivalent. Also, we present a correspondence between almost periodic functions defined in quantum calculus and N₀, proving several important properties for this class of functions. We investigate the existence of almost periodic solutions of linear and nonlinear q-difference equations. Finally, we provide some examples of almost periodic functions in quantum calculus.

An Introduction To Psychological Statistics, Garett C. Foster, David Lane, David Scott, Mikki Hebl, Rudy Guerra, Dan Osherson, Heidi Zimmer

Open Educational Resources Collection

This work has been superseded by Introduction to Statistics in the Psychological Sciences available from https://irl.umsl.edu/oer/25/.

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We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness. The study of statistics involves math and relies …

The Compensation For Few Clusters In Clustered Randomized Trials With Binary Outcomes, Lily Stalter

Mathematics & Statistics ETDs

Cluster randomized trials are increasingly popular in epidemiological and medical research. When analyzing the data from such studies it is imperative that the hierarchical structure of the data be taken into account. Multilevel logistic regression is used to analyze clustered data with binary outcomes. Previous literature shows that a greater number of clusters is more important than a large number of subjects per cluster. This paper investigates if it is possible to compensate for the increased bias found for parameter estimates when the number of clusters is decreased. A simulation study was conducted where the absolute percent relative bias for …