Statistics and Probability Commons^™

Bimodality Revisited, Thomas R. Knapp

Journal of Modern Applied Statistical Methods

Degree of bimodality is an important feature of a frequency distribution, because it could suggest heterogeneity, such as polarization or two underlying distributions combined into one. The literature contains several measures of bimodality. This article attempts to summarize most of those measures, with their attendant advantages and disadvantages.

Type I Error Rates Of The Kenward-Roger Adjusted Degree Of Freedom F-Test For A Split-Plot Design With Missing Values, Miguel A. Padilla, James Algina

Journal of Modern Applied Statistical Methods

The Type I error rate of the Kenward-Roger (KR) test, implemented by PROC MIXED in SAS, was assessed through a simulation study for a one between- and one within-subjects factor split-plot design with ignorable missing values and covariance heterogeneity. The KR test controlled the Type I error well under all of the simulation factors, with all estimated Type I error rates between .040 and .075. The best control was for testing the between-subjects main effect (error rates between .041 and .057) and the worst control was for the between-by-within interaction (.040 to .075). The simulated factors had very small effects …

Comparison Of The T Vs. Wilcoxon Signed-Rank Test For Likert Scale Data And Small Samples, Gary E. Meek, Ceyhun Ozgur, Kenneth Dunning

Journal of Modern Applied Statistical Methods

The one sample t-test is compared with the Wilcoxon Signed-Rank test for identical data sets representing various Likert scales. An empirical approach is used with simulated data. Comparisons are based on observed error rates for 27,850 data sets. Recommendations are provided.

Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara

Journal of Modern Applied Statistical Methods

The aim of this article is to obtain and compare confidence intervals for the mean of an exponential distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for parameters of exponential population are derived. Using exponential data, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with Fisher Matrix bounds method. It is shown that the proposed approximate Bayesian approach relies only on the observations. The Fisher Matrix bounds method, that uses the z-table, does not always yield the best confidence intervals, and the proposed approach often performs better.

Beta-Weibull Distribution: Some Properties And Applications To Censored Data, Carl Lee, Felix Famoye, Olugbenga Olumolade

Journal of Modern Applied Statistical Methods

Some properties of a four-parameter beta-Weibull distribution are discussed. The beta-Weibull distribution is shown to have bathtub, unimodal, increasing, and decreasing hazard functions. The distribution is applied to censored data sets on bus-motor failures and a censored data set on head-and-neck-cancer clinical trial. A simulation is conducted to compare the beta-Weibull distribution with the exponentiated Weibull distribution.

Detection And Estimation Of A Mixture In Power Law Processes For A Repairable System, Ni Wang, Paul Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

The power law process has proved to be a useful tool in characterizing the failure process of repairable systems. This paper presents a procedure for detecting and estimating a mixture of reliable and unreliable (defective) systems. The test of a mixture, based on a simple likelihood ratio, is illustrated with truncated failure data for copy machines. Bootstrap methods are used to gauge the estimation uncertainty, and optimal decisions for system replacement are determined based on the observed likelihood.

Canonical Correlation And Correspondence Analysis Of Longitudinal Data, Jayesh Srivastava

Mathematics & Statistics Theses & Dissertations

Assessing the relationship between two sets of multivariate vectors is an important problem in statistics. Canonical correlation coefficients are used to study these relationships. Canonical correlation analysis (CCA) is a general multivariate method that is mainly used to study relationships when both sets of variables are quantitative. When the variables are qualitative (categorical), a technique called correspondence analysis (CA) is used. Canonical correspondence analysis (CCPA) is used to deal with the case when one set of variables is categorical and the other set is quantitative. By exploiting the interrelationships between these three techniques we first provide a theoretical basis for …

A Multivariate Magnitude Robust Control Chart For Mean Shift Detection And Change Point Estimation, Ryan M. Harrell

Theses and Dissertations

Statistical control charts are often used to detect a change in an otherwise stable process. This process may contain several variables affecting process stability. The goal of any control chart is to detect an out-of-control state quickly and provide insight on when the process actually changed. This reduces the off-line time the quality engineer spends assigning causality. In this research, a multivariate magnitude robust chart (MMRC) was developed using a change point model and a likelihood-ratio approach. Here the process is considered in-control until one or more normally distributed process variables permanently and suddenly shifts to out-of-control, stable value. Using …

Professionalism In The Air Force: A Comparative Analysis Of Commissioned Officers With Non-Commissioned Officers, Edward K. Boyd

Theses and Dissertations

Decades ago, military sociologists predicted a rising trend among officers away from traditional institutional military values and toward more economically-based occupational values due to the effects of the transition from a conscription-based military to an all-volunteer force. Subsequent empirical research resulted in data that supports such predictions. More recent researchers have suggested that in addition to the all-volunteer force, an increase on technology may also accelerate the trend toward occupationalism and away from traditional institutional military values and the warrior ethos that typically define successful military organizations. The officer corps may be particularly vulnerable to occupationalism due to increased technical …

Foreigners' Fate In America's Courts: Empirical Legal Research, Kevin M. Clermont, Theodore Eisenberg

Cornell Law Faculty Publications

This article revisits the controversy regarding how foreigners fare in U.S. courts. The available data, if taken in a sufficiently big sample from numerous case categories and a range of years, indicate that foreigners have fared better in the federal courts than their domestic counterparts have fared. Thus, the data offer no support for the existence of xenophobic bias in U.S. courts. Nor do they establish xenophilia, of course. What the data do show is that case selection drives the outcomes for foreigners. Foreigners’ aversion to U.S. forums can elevate the foreigners’ success rates, when measured as a percentage of …

An Evaluation Of Organizational And Experience Factors Affecting The Perceived Transfer Of U.S. Air Force Basic Combat Skills Training, Shirley D. Crow

Theses and Dissertations

The United States Air Force is in a state of transformation. Due to ongoing operations in Iraq and Afghanistan, the focus of Basic Military Training is shifting to basic combat skills, or the skills needed to survive and operate in a hostile environment. In this study, basic combat skills training was evaluated using a number of training factors that potentially affect trainees’ perception of training transfer, or their ability to apply the skills they learned in training on the job or in a hostile environment. The analysis used structural equation modeling to evaluate the paths between each of the factors …

Predicting Argentine Jet Fuel Prices, Juan A. Salaverry

Theses and Dissertations

Oil distillates are considered important elements to accomplish the missions of the Argentine Air Force (AAF). Of all oil products consumed by the AAF, jet fuel is the resource with highest demand and at the end of the day the most expensive support item procured by the Argentine Air Force. Accurate predictions of Argentine jet fuel prices are necessary to improve AAF financial and logistics planning. This thesis presents a systematic, statistical regression approach to forecast Argentine jet fuel prices. The application of this methodology has allowed us to obtain a very useful model that utilizes information available on the …

Step-Up Simultaneous Tests For Identifying Active Effects In Orthogonal Saturated Designs, Samuel S. Wu, Weizhen Wang

Mathematics and Statistics Faculty Publications

A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given alpha level in the strong sense.

A Robust Measure Of Correlation Between Two Genes On A Microarray, Johanna S. Hardin, Aya Mitani '06, Leanne Hicks, Brian Vankoten

Pomona Faculty Publications and Research

Background

The underlying goal of microarray experiments is to identify gene expression patterns across different experimental conditions. Genes that are contained in a particular pathway or that respond similarly to experimental conditions could be co-expressed and show similar patterns of expression on a microarray. Using any of a variety of clustering methods or gene network analyses we can partition genes of interest into groups, clusters, or modules based on measures of similarity. Typically, Pearson correlation is used to measure distance (or similarity) before implementing a clustering algorithm. Pearson correlation is quite susceptible to outliers, however, an unfortunate characteristic when dealing …

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

On The Exact Multiplicity Of Solutions For Boundary-Value Problems Via Computing The Direction Of Bifurcations, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

On The Direction Of Pitchfork Bifurcation, Xiaojie Hou, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result.

A Comparison Of Graphical Methods For Assessing The Proportional Hazards Assumptions In The Cox Model, Inger Persson, Harry J. Khamis

Mathematics and Statistics Faculty Publications

Six graphical procedures to check the assumption of proportional hazards for the Cox model are described and compared. A new way of comparing the graphical procedures using a Kolmogorov-Smirnov like maximum deviation criterion for rejection is derived for each procedure. The procedures are evaluated in a simulation study under proportional hazards and five different forms of nonproportional hazards: (1) increasing hazards, (2) decreasing hazards, (3) crossing hazards, (4) diverging hazards, and (5) nonmonotonic hazards. The procedures are compared in the two-sample case corresponding to two groups with different hazard functions. None of the procedures under consideration require partitioning of the …

Projective-Planar Signed Graphs And Tangled Signed Graphs, Dan Slilaty

Mathematics and Statistics Faculty Publications

A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained by taking a projective-planar signed graph or a copy of −K5" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">−K5 and then taking 1-, 2-, and 3-sums with balanced signed grap

Degradation Models And Implied Lifetime Distributions, Suk Joo Bae, Way Kuo, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In experiments where failure times are sparse, degradation analysis is useful for the analysis of failure time distributions in reliability studies. This research investigates the link between a practitioner's selected degradation model and the resulting lifetime model. Simple additive and multiplicative models with single random effects are featured. Results show that seemingly innocuous assumptions of the degradation path create surprising restrictions on the lifetime distribution. These constraints are described in terms of failure rate and distribution classes.

Statistical Models For Hot Electron Degradation In Nano-Scaled Mosfet Devices, Suk Joo Bae, Seong-Joon Kim, Way Kuo, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In a MOS structure, the generation of hot carrier interface states is a critical feature of the item's reliability. On the nano-scale, there are problems with degradation in transconductance, shift in threshold voltage, and decrease in drain current capability. Quantum mechanics has been used to relate this decrease to degradation, and device failure. Although the lifetime, and degradation of a device are typically used to characterize its reliability, in this paper we model the distribution of hot-electron activation energies, which has appeal because it exhibits a two-point discrete mixture of logistic distributions. The logistic mixture presents computational problems that are …

The Flight From Arbitration: An Empirical Study Of Ex Ante Arbitration Clauses In The Contracts Of Publicly Held Companies, Theodore Eisenberg, Geoffrey P. Miller

Cornell Law Faculty Publications

Informed parties bargaining for their mutual advantage will tend to agree to provisions that maximize the social surplus. Such bargaining includes provisions regarding the resolution of disputes that might arise under the contract. Thus, if a form of alternative dispute resolution, such as binding arbitration, provides greater social benefits than litigation, the dynamics of the process should tend to induce the parties to include a clause submitting future disputes to arbitration. This Article studies the actual contracting practices of large, sophisticated actors with respect to arbitration clauses. We examined over 2800 contracts, filed with the Securities Exchange Commission (SEC) in …

Hierarchical Linear Modeling In Organizational Research: Longitudinal Data Outside The Context Of Growth Modeling, Irvin Sam Schonfeld, David Rindskopf

Publications and Research

Organizational researchers, including those carrying out occupational stress research, often conduct longitudinal studies. Hierarchical linear modeling (HLM; also known as multilevel modeling and random regression) can efficiently organize analyses of longitudinal data by including within- and between-person levels of analysis. A great deal of longitudinal research has been conducted in the context of growth studies in which change in the dependent variable is examined in relation to the passage of time. HLM can treat longitudinal data, including data outside the context of the growth study, as nested data, reducing the problem of censoring. Within-person equation coefficients can represent the impact …

Modeling And Efficient Estimation Of Intra-Family Correlations, Roy Sabo

Mathematics & Statistics Theses & Dissertations

Familial data occur when observations are taken on multiple members of the same family. Due to relationships between these members, both genetic and by cohabitation, their response variables will likely exhibit some form of dependence. Most of the existing literature models this dependence with an equicorrelated structure. This structure is appropriate when the dependencies between family members are similar, such as in genetic studies, but not in cases where we expect the dependencies to differ, such as behavioral comparisons across different age groups. In this dissertation we first discuss an alternative structure based upon first-order autoregressive correlation. Specifically we create …

Numerical And Asymptotical Study Of Three-Dimensional Wave Packets In A Compressible Boundary Layer, Eric Forgoston, Michael Viergutz, Anatoli Tumin

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initialvalue problem. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as Mode S and Mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectra are analyzed numerically for a hypersonic flow. A comprehensive study of the spectrum is performed, including Reynolds number, Mach number and temperature …

A Conversation With Harry Martz, Paul H. Kvam

Department of Math & Statistics Faculty Publications

Harry F. Martz was born June 16, 1942 and grew up in Cumberland, Maryland. He received a Bachelor of Science degree in mathematics (with a minor in physics) from Frostburg State University in 1964, and earned a Ph.D. in statistics at Virginia Polytechnic Institute and State University in 1968. He started his statistics career at Texas Tech University's Department of Industrial Engineering and Statistics right after graduation. In 1978, he joined the technical staff at Los Alamos National Laboratory (LANL) in Los Alamos, New Mexico after first working as Full Professor in the Department of Industrial Engineering at Utah State …

Ex Ante Choices Of Law And Forum: An Empirical Analysis Of Corporate Merger Agreements, Theodore Eisenberg, Geoffrey P. Miller

Cornell Law Faculty Publications

Legal scholars have focused much attention on the incorporation puzzle—why business corporations so heavily favor Delaware as the site of incorporation. This paper suggests that the focus on the incorporation decision overlooks a broader but intimately related set of questions. The choice of Delaware as a situs of incorporation is, effectively, a choice of law decision. A company electing to charter in Delaware selects Delaware law (and authorizes Delaware courts to adjudicate legal disputes) regarding the allocation of governance authority within the firm. In this sense, the incorporation decision is fundamentally similar to any setting in which a company selects …

Allometric Extension For Multivariate Regression Models, Thaddeus Tarpey, Christopher T. Ivey

Mathematics and Statistics Faculty Publications

In multivariate regression, interest lies on how the response vector depends on a set of covariates. A multivariate regression model is proposed where the covariates explain variation in the response only in the direction of the first principal component axis. This model is not only parsimonious, but it provides an easy interpretation in allometric growth studies where the first principal component of the log-transformed data corresponds to constants of allometric growth. The proposed model naturally generalizes the two–group allometric extension model to the situation where groups differ according to a set of covariates. A bootstrap test for the model is …

Theory Of Effectiveness Measurement, Richard K. Bullock

Theses and Dissertations

Effectiveness measures provide decision makers feedback on the impact of deliberate actions and affect critical issues such as allocation of scarce resources, as well as whether to maintain or change existing strategy. Currently, however, there is no formal foundation for formulating effectiveness measures. This research presents a new framework for effectiveness measurement from both a theoretical and practical view. First, accepted effects-based principles, as well as fundamental measurement concepts are combined into a general, domain independent, effectiveness measurement methodology. This is accomplished by defining effectiveness measurement as the difference, or conceptual distance from a given system state to some reference …

Statistical Approach To Background Subtraction For Production Of High-Quality Silhouettes For Human Gait Recognition, Jennifer J. Samler

Theses and Dissertations

This thesis uses a background subtraction to produce high-quality silhouettes for use in human identification by human gait recognition, an identification method which does not require contact with an individual and which can be done from a distance. A statistical method which reduces the noise level is employed resulting in cleaner silhouettes which facilitate identification. The thesis starts with gathering video data of individuals walking normally across a background scene. From there the video is converted into a sequence of images that are stored as joint photographic experts group (jpeg) files. The background is subtracted from each image using a …