Applied Statistics Commons^™

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang

Mathematics and Statistics Faculty Publications

We show that any C^1,1 solution to the uniformly elliptic equation F(D²u) = 0 must belong to C^2,α, if the equation has the Liouville property.

Absolutely Continuous Jacobi Operators, Steen Pedersen

Mathematics and Statistics Faculty Publications

No abstract provided.

Domain Functionals And Exit Times For Brownian Motion, Chaocheng Huang, David Miller

Mathematics and Statistics Faculty Publications

Two domain functionals describing the averaged expectation of exit times and averaged variance of exit times of Brownian motion from a domain, respectively, are studied.

Nonparametric Estimation Of A Distribution Subject To A Stochastic Precedence Constraint, Miguel A. Arcones, Paul H. Kvam, Francisco J. Samaniego

Department of Math & Statistics Faculty Publications

For any two random variables X and Y with distributions F and G defined on [0,∞), X is said to stochastically precede Y if P(X≤Y) ≥ 1/2. For independent X and Y, stochastic precedence (denoted by X≤_spY) is equivalent to E[G(X–)] ≤ 1/2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a …

Discrete Predictive Analysis In Probabilistic Safety Assessment, Paul Kvam, J. Glenn Miller

Department of Math & Statistics Faculty Publications

This paper presents methods for predicting future numbers of component failures for probabilistic safety assessments (PSAs). The research is motivated and illustrated by discrete failure data from the nuclear industry, including failure counts for emergency diesel generators, pumps, and motor operated valves. Failure counts are modeled with Poisson and binomial distributions. Multiple-failure environments create extra problems for predictive inference, and are a primary focus of this paper. Common cause failures (CCFs), in particular, refer to the simultaneous failure of system components due to an external event. CCF prediction is investigated, and approximate inference methods are derived for various CCF models.

Common Cause Failure Prediction Using Data Mapping, Paul H. Kvam, J. Glenn Miller

Department of Math & Statistics Faculty Publications

To estimate power plant reliability, a probabilistic safety assessment might combine failure data from various sites. Because dependent failures are a critical concern in the nuclear industry, combining failure data from component groups of different sizes is a challenging problem. One procedure, called data mapping, translates failure data across component group sizes. This includes common cause failures, which are simultaneous failure events of two or more components in a group. In this paper, we present methods for predicting future plant reliability using mapped common cause failure data. The prediction technique is motivated by discrete failure data from emergency diesel generators …

Mixed Signals: Rational-Choice Theories Of Social Norms And The Pragmatics Of Explanation, W. Bradley Wendel

Cornell Law Faculty Publications

The question of how societies secure cooperation and order in the absence of state enforced sanctions has long vexed law and economics scholars. Recently the concept of social norms--informally enforced rules of behavior--has occupied the attention of a large number of these theorists, who are concerned with understanding why economically rational actors would bother to follow rules whose costs seem to outweigh their benefits. Because of the prestige (or at least trendiness) of law and economics, it seems that now everyone in the legal academy is talking about social norms. This burgeoning scholarship is closely related to a wider concern …

Control Of Error Rates In Adaptive Analysis Of Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss

Mathematics and Statistics Faculty Publications

Individual and simultaneous confidence intervals using the data adaptively are constructed for the effects in orthogonal saturated designs under the assumption of effect sparsity. The minimum coverage probabilities of the intervals are equal to the nominal level 1 - α.

Probing "Life Qualification" Through Expanded Voir Dire, John H. Blume, Sheri Lynn Johnson, A. Brian Threlkeld

Cornell Law Faculty Publications

The conventional wisdom is that most trials are won or lost in jury selection. If this is true, then in many capital cases, jury selection is literally a matter of life or death. Given these high stakes and Supreme Court case law setting out standards for voir dire in capital cases, one might expect a sophisticated and thoughtful process in which each side carefully considers which jurors would be best in the particular case. Instead, it turns out that voir dire in capital cases is woefully ineffective at the most elementary task--weeding out unqualified jurors.

Empirical evidence reveals that many …

Forecasting Life And Death: Juror Race, Religion, And Attitude Toward The Death Penalty, Theodore Eisenberg, Stephen P. Garvey, Martin T. Wells

Cornell Law Faculty Publications

Determining whether race, sex, or other juror characteristics influence how capital case jurors vote is difficult. Jurors tend to vote for death in more egregious cases and for life in less egregious cases no matter what their own characteristics. And a juror's personal characteristics may get lost in the process of deliberation because the final verdict reflects the jury's will, not the individual juror's. Controlling for the facts likely to influence a juror's verdict helps to isolate the influence of a juror's personal characteristics. Examining each juror's first sentencing vote reveals her own judgment before the majority works its will. …

Statistical Modeling And Inference Regarding Risk In Case Control Studies, Deborah Kay Shepherd

Doctoral Dissertations

Some of the common measures of risk used m epidemiology today are the relative risk, the odds ratio, the attributable risk, and the chi-square goodness of fit test. All of these measures have their shortcomings. A new approach to measuring risk in case-control studies is to use the unitless measure of the coefficient of variation of incidence of disease over the risk categories, kˆ2, first proposed by Begg et al. (1998). Begg et al. (1998), also showed that the product of multiple risk factors may be compared to an overall measure of the square of the coefficient of variation …

Statistical Properties Of Maximum Likelihood Estimates For Accelerated Lifetime Data Under The Weibull Model, Mahmoud A. Yousef

Doctoral Dissertations

Pipe rehabilitation liners are often installed in host pipes that lie below the water table. As such, they are subjected to external hydrostatic pressure. The external pressure leads to early deformation in the liners, which could ultimately lead to its failing or buckling before its expected service lifetime is achieved. Experiments involving long term buckling behavior of liners are typically accelerated lifetime testing procedures. In an accelerated testing procedure a liner is subjected to a constant external hydrostatic pressure and observed until it fails or for a certain time, t whichever occurs first. Liners that do not fail at time …

Calculating Rank-In-Class Numbers: The Impact Of Grading Differences Among Law School Teachers, Paul T. Wangerin

Journal of Legal Education

No abstract provided.

Pen Or Printer: Can Students Afford To Handwrite Their Exams?, Kif Augustine-Adams, Suzanne B. Hendrix, James R. Rasband

Journal of Legal Education

No abstract provided.

Minimum Distance Estimation For Time Series Analysis With Little Data, Hakan Tekin

Theses and Dissertations

Minimum distance estimate is a statistical parameter estimate technique that selects model parameters that minimize a good-of-fit statistic. Minimum distance estimation has been demonstrated better standard approaches, including maximum likelihood estimators and least squares, in estimating statistical distribution parameters with very small data sets. This research applies minimum distance estimation to the task of making time series predictions with very few historical observations. In a Monte Carlo analysis, we test a variety of distance measures and report the results based on many different criteria. Our analysis tests the robustness of the approach by testing its ability to make predictions when …

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

Ranked Set Sampling From Location-Scale Families Of Symmetric Distributions, Ram C. Tiwari, Paul H. Kvam

Department of Math & Statistics Faculty Publications

Statistical inference based on ranked set sampling has primarily been motivated by nonparametric problems. However, the sampling procedure can provide an improved estimator of the population mean when the population is partially known. In this article, we consider estimation of the population mean and variance for the location-scale families of distributions. We derive and compare different unbiased estimators of these parameters based on independent replications of a ranked set sample of size n. Large sample properties, along with asymptotic relative efficiencies, help identify which estimators are best suited for different location-scale distributions.

The Deadly Paradox Of Capital Jurors, Theodore Eisenberg, Stephen P. Garvey, Martin T. Wells

Cornell Law Faculty Publications

We examine support for the death penalty among a unique group of respondents: one hundred and eighty-seven citizens who actually served as jurors on capital trials in South Carolina. Capital jurors support the death penalty as much as, if not more than, members of the general public. Yet capital jurors, like poll respondents, harbor doubts about the penalty's fairness. Moreover, jurors--black jurors and Southern Baptists in particular--are ready to abandon their support for the death penalty when the alternative to death is life imprisonment without the possibility of parole, especially when combined with a requirement of restitution. Support for the …

Heckman's Methodology For Correcting Selectivity Bias : An Application To Road Crash Costs, Margaret Giles

Research outputs pre 2011

Aggregate road crash costs are traditionally determined using average costs applied to incidence figures found in Police-notified crash data. Such data only comprise a non-random sample of the true population of road crashes, the bias being due to the existence of crashes that are not notified to the Police. The traditional approach is to label the Police-notified sample as 'non-random' thereby casting a cloud over data analyses using this sample. Heckman however viewed similar problems as 'omitted variables' problems in that the exclusion of some observations in a systematic manner (so-called selectivity bias) has inadvertently introduced the need for an …

On The Evolution Of Probability-Weighting Function And Its Impact On Gambling, Steven Li, Yun Hsing Cheung

Research outputs pre 2011

It is well known that individuals treat losses and gains differently and there exists non-linearity in probability. The asymmetry between gains and losses is highlighted by the reflection effect. The non-linearity in probability is described by the curvature of the probability-weighting function. This paper studies the evolution of the probability-weighting function. It is assumed that the probability weighting for an individual follows a mean-reverting stochastic process. The Monte Carlo simulation technique is employed to study the evolution of the weighting function. The evolution of the probability- weighting function implies that an individual does not treat gains or losses consistently over …

Change Of Support Correction In Mineral Resource Estimation, Marek J. Janas

Theses: Doctorates and Masters

The success of any mining operation greatly, if not entirely, depends on the accuracy of prediction of recoverable mining reserves. However, prior to mining, knowledge about the distribution of the Selective Mining Unit (SMU) is limited. The SMU represents the volume on which extraction of ore takes place and on which recoverable mining reserves are based. Realistic recoverable reserve estimates can be obtained from the grade-tonnage curve that corresponds to the unknown distribution of the SMU rather than to the distribution of exploration sample data. In general, if the reserve calculation, at the given cut-off grade, is based upon exploration …

Commuting Self-Adjoint Extensions Of Symmetric Operators Defined From The Partial Derivatives, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(∂/∂x_j):j=1,...,d} with domain C^∞_c(Ω) where the self-adjointness is defined relative to L²(Ω), and Ω is a given open subset of R^d.

The Expected Wet Period Of Finite Dam With Exponential Inputs, Eui Yong Lee, Kimberly Kinateder

Mathematics and Statistics Faculty Publications

We use martingale methods to obtain an explicit formula for the expected wet period of the finite dam of capacity V, where the amounts of inputs are i.i.d exponential random variables and the output rate is one, when the reservoir is not empty. As a consequence, we obtain an explicit formula for the expected hitting time of either 0 or V and a new expression for the distribution of the number of overflows during the wet period, both without the use of complex analysis.

A Nonlinear Parabolic Equation Modelling Surfactant Diffusion, Xinfu Chen, Chaocheng Huang, Jennifer Zhao

Mathematics and Statistics Faculty Publications

An initial-boundary value problem for nonlinear parabolic equations modelling surfactant diffusions is investigated. The boundary conditions are of nonlinear adsorptive types, and the initial value has a single point jump. We study the well-posedness of the problem, the convergence of a numerical scheme, and the regularity as well as quantitative behaviour of solutions.

Permitting Jury Discussions During Trial: Impact Of The Arizona Reform, Paula Hannaford-Agor, Valerie P. Hans, G. Thomas Munsterman

Cornell Law Faculty Publications

A field experiment tested the effect of an Arizona civil jury reform that allows jurors to discuss evidence among themselves during the trial. Judges, jurors, attorneys, and litigants completed questionnaires in trials randomly assigned to either a Trial Discussions condition, in which jurors were permitted to discuss the evidence during trial, or a No Discussions condition, in which jurors were prohibited from discussing evidence during trial according to traditional admonitions. Judicial agreement with jury verdicts did not differ between conditions. Permitting jurors to discuss the evidence did affect the degree of certainty that jurors reported about their preferences at the …

Empirical Methods And The Law, Theodore Eisenberg

Cornell Law Faculty Publications

One can divide empirical analysis of legal issues into three major branches: (1) the use of scientific empirical analysis by litigants to attempt to prevail in individual cases, (2) the use of social scientific empirical analysis in individual cases, and (3) the use of the empirical methods to describe the legal system’s operation. The first two uses present difficulties that reflect a fundamental limitation on using statistical methods in law: the difference between establishing statistical association and establishing actual causation in an individual case filtered through our adversary legal system. The third use encounters no such obstacle and can aid …

The Timing Of Opinion Formation By Jurors In Civil Cases: An Empirical Examination, Paula Hannaford-Agor, Valerie P. Hans, Nicole L. Mott, G. Thomas Munsterman

Cornell Law Faculty Publications

The question of when and how jurors form opinions about evidence presented at trial has been the focus of seemingly endless speculation. For lawyers, the question is how to capture the attention and approval of the jury at the earliest possible point in the trial. Their goal is to maximize the persuasiveness of their arguments--or at least to minimize the persuasiveness of those of the opposing side. Judges, in contrast, are more concerned about prejudgment. They regularly admonish jurors to suspend judgment until after all the evidence has been presented and after the jurors have been instructed on the law. …

The Emotional Economy Of Capital Sentencing, Stephen P. Garvey

Cornell Law Faculty Publications

You often hear that one reason capital jurors condemn capital defendants is that jurors don't empathize with defendants. And one reason they don't empathize is that the process of capital sentencing is rigged against empathy. Using data from the South Carolina segment of the Capital Jury Project, I try to examine the role emotion plays in capital sentencing.

Without entering here all the important and necessary caveats, I find that the self-reported emotional responses jurors have toward capital defendants run the gamut from sympathy and pity at one extreme, to disgust, anger, and fear at the other. What causes these …

Associations Among Hospital Capacity, Utilization, And Mortality Of Us Medicare Beneficiaries, Controlling For Sociodemographic Factors., E. S. Fisher, J. E. Wennberg, T. A. Stukel, J. S. Skinner, S. M. Sharp

Dartmouth Scholarship

To explore whether geographic variations in Medicare hospital utilization rates are due to differences in local hospital capacity, after controlling for socioeconomic status and disease burden, and to determine whether greater hospital capacity is associated with lower Medicare mortality rates.