Statistics and Probability Commons^™

Structure-Function Relationships In The Pulmonary Arterial Tree, Christopher A. Dawson, Gary S. Krenz, Kelly Lynn Karau, Steven Thomas Haworth, Christopher C. Hanger, John H. Linehan

Mathematics, Statistics and Computer Science Faculty Research and Publications

Knowledge of the relationship between structure and function of the normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of the vascular remodeling that accompanies pulmonary vascular diseases. In an effort to provide a means for relating the measurable vascular geometry and vessel mechanics data to the mean pressure-flow relationship and longitudinal pressure profile, we present a mathematical model of the pulmonary arterial tree. The model is based on the observation that the normal pulmonary arterial tree is a bifurcating tree in which the parent-to-daughter diameter ratios at a bifurcation and vessel distensibility are …

Kriging Puerto Rico Rainfall, Gary B. Hughes

Statistics

In Earth science research, climatic conditions can have significant effects on dynamic processes. For example, the growth of forests is affected by temperature, rainfall and other climatic variables. However, these climate parameters are rarely measured at the forest stands whose growth is being investigated. The climate conditions are measured at nearby weather stations, though, and it is a common approach to use the weather station data to ‘predict’ the climate at the study site

Breeding And Genetics 5: Survival Analysis/Threshold Models, Applications In Survival Analysis, Stephen D. Kachman

Department of Statistics: Faculty Publications

Survival or failure time traits such as herd life and days open are both important economically and pose a number of challenges to an analysis based on linear mixed models. The main features of a survival trait are that it is the time until some event occurs, and some of the observations are censored. Survival models and the associated estimation procedures provide a flexible means of modeling survival traits. In this paper I will discuss the application of survival analysis based on the Weibull distribution. The components that make up a survival model will be presented along with their interpretation. …

The Stable Manifold Theorem For Stochastic Differential Equations, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow

Articles and Preprints

We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itô-type equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution. For Stratonovich SDEs, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating SDE. The proof of the stable manifold theorem is based …

Ua56/1 Facts At A Glance, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

03. Preface Of Design And Analysis Of Experiments - 1st Edition, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

Preface of the first edition of Design and Analysis of Experiments.

Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng

Mathematics and Statistics Faculty Publications

A report of progress in linear and nonlinear partial differential equations, microlocal analysis, singular partial differential operators, spectral analysis and hyperfunction theory. The papers aretaken from a conference on partial differential equations and their applications, held in Wuhan.

Invariant Measures For Set-Valued Dynamical Systems, Walter Miller, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

A continuous map on a compact metric space, regarded as a dynamical system by iteration, admits invariant measures. For a closed relation on such a space, or, equivalently, an upper semicontinuous set-valued map, there are several concepts which extend this idea of invariance for a measure. We prove that four such are equivalent. In particular, such relation invariant measures arise as projections from shift invariant measures on the space of sample paths. There is a similarly close relationship between the ideas of chain recurrence for the set-valued system and for the shift on the sample path space. ©1999 American Mathematical …

Modeling Of Catastrophic Events With Applications To Insurance, Mary Noga

Presidential Scholars Theses (1990 – 2006)

Tornadoes effect every area in the continental United States. There are great differences in the number and amount of damages caused by tornadoes in different regions. The mid-west is nicknamed tornado alley, because of the large number of tornadoes in this region each year. A tornado is commonly described as a "rapidly rotating, slender, funnel-shaped cloud."

The National Climatic Data Center (NCDC) has data on tornadoes over the past four years. This data includes the state, date, and damage done by each tornado. For the purpose of this study a data-set including all tornadoes causing over ten million in damages …

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn

Mathematics Faculty Publications

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring Axiom.

On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for .

Bayes Estimation Of A Distribution Function Using Ranked Set Samples, Paul H. Kvam, Ram C. Tiwari

Department of Math & Statistics Faculty Publications

Aranked set sample (RSS), if not balanced, is simply a sample of independent order statistics generated from the same underlying distribution F. Kvam and Samaniego (1994) derived maximum likelihood estimates of F for a general RSS. In many applications, including some in the environmental sciences, prior information about F is available to supplement the data-based inference. In such cases, Bayes estimators should be considered for improved estimation. Bayes estimation (using the squared error loss function) of the unknown distribution function F is investigated with such samples. Additionally, the Bayes generalized maximum likelihood estimator (GMLE) is derived. An iterative scheme based …

Nonparametric Estimation Of The Survival Function Based On Censored Data With Additional Observations From The Residual Distribution, Paul Kvam, Harshinder Singh, Ram C. Tiwari

Department of Math & Statistics Faculty Publications

We derive the nonparametric maximum likelihood estimator (NPMLE) of the distribution of the test items using a random, right-censored sample combined with an additional right-censored, residual-lifetime sample in which only lifetimes past a known, fixed time are collected. This framework is suited for samples for which individual test data are combined with left-truncated and randomly censored data from an operating environment. The NPMLE of the survival function using the combined sample is identical to the Kaplan-Meier product-limit estimator only up to the time at which the test items corresponding to the residual sample were known to survive. The limiting distribution …

A Quantile‐Based Approach For Relative Efficiency Measurement, Paul M. Griffin, Paul H. Kvam

Department of Math & Statistics Faculty Publications

Two popular approaches for efficiency measurement are a non‐stochastic approach called data envelopment analysis (DEA) and a parametric approach called stochastic frontier analysis (SFA). Both approaches have modeling difficulty, particularly for ranking firm efficiencies. In this paper, a new parametric approach using quantile statistics is developed. The quantile statistic relies less on the stochastic model than SFA methods, and accounts for a firm's relationship to the other firms in the study by acknowledging the firm's influence on the empirical model, and its relationship, in terms of similarity of input levels, to the other firms.

Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh

Department of Math & Statistics Faculty Publications

Standard inference procedures assume a random sample from a population with density f_μ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density f_μ^w(x) that is proportional to w(x)f_μ(x). In this paper, we assume that f_μ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the k^th order …

The Association Of Fluid Intake With Total Natural-Cause Mortality, Coronary Heart Disease And Fatal Stroke, Jacqueline Chung Lun Chan

Loma Linda University Electronic Theses, Dissertations & Projects

Hypohydration may be more widespread than realized since it does not always arouse a sense of thirst. When thirst is felt, it is often ignored, or satisfied before euhydration is achieved. There is growing evidence indicating that hypohydration contributes to acute and chronic illnesses, and to rheological factors associated with coronary heart disease (CHD) and stroke. Therefore the relationship of fluid intake with risk of total natural-cause mortality, CHD and stroke death was examined using data on 34,192 white, non-Hispanic participants in the Adventist Health Study.

Among the 27,342 reporting no CHD, stroke or diabetes at baseline, during six years …

Body Weight And Mortality Among Adults Who Never Smoked, Pramil N. Singh

Loma Linda University Electronic Theses, Dissertations & Projects

Most prospective studies identify an increased mortality risk for adults of high body mass index (> 27 kg/m²) that is commonly attributed to the effects of excess body fat, and also identify an increased mortality risk for adults of low body mass index (< 21 kg/m²), an association that, if causal among healthy adults, is without adequate pathophysiologic support.

In this dissertation, I have conducted three studies that continue the investigation of adiposity in relation to mortality among never-smoking adults of the California Seventh-day Adventist population. Among never-smoking adults of the Adventist Mortality Study (1960-1985), the relation between …

The Predictability Of Punitive Damages Awards In Published Opinions, The Impact Of Bmw V. Gore On Punitive Damages Awards, And Forecasting Which Punitive Awards Will Be Reduced, Theodore Eisenberg, Martin T. Wells

Cornell Law Faculty Publications

This article assesses the relation between compensatory damages and punitive damages in cases leading to published opinions and BMW v. Gore's impact on the patterns of punitive damages awards in these opinions. We find that punitive damages awards are considerably higher in cases leading to published opinions than in trial level cases. But the correlation between compensatory and punitive awards found in trial level data persists in published opinions and is all but indistinguishable from the correlation in trial level data. We find no significant difference in the pattern of awards before and after BMW and no significant difference …

Judicial Decisionmaking In Federal Products Liability Cases, 1978-1997, Theodore Eisenberg

Cornell Law Faculty Publications

In 1992, Professor James Henderson and I wrote that, throughout the 1980s, a quiet, pro-defendant revolution in products liability had occurred. That revolution was likely largely the product of a "widespread, independent shift in judicial attitudes." It was not discernable in cases tried before juries. The federal data used in that study were available through 1989. Also in 1992, using the same database, Professor Kevin Clermont and I wrote about the surprising relation between plaintiff win rates in judge and jury trials in products liability cases. Plaintiffs prevailed at a higher rate before judges than they did before juries. Comparable …

How Do Judges Think About Risk?, W. Kip Viscusi

Vanderbilt Law School Faculty Publications

A sample of almost 100 judges exhibited well-known patterns of biases in risk beliefs and reasonable implicit values of life. These biases and personal preferences largely do not affect attitudes toward judicial risk decisions, though there are some exceptions, such as ambiguity aversion, misinterpretation of negligence rules, and retrospective risk assessments in accident cases, which is a form of hindsight bias. Although judges avoided many pitfalls exhibited by jurors and the population at large, they nevertheless exhibited systematic errors, particularly for small probability-large loss events. These findings highlighted the importance of judicial review and the input of expert risk analysts …

Description Of Non-Precision In Experimental Field Scores, Adedapo Odulaja

All Peer-Reviewed Publications

Visual assessments are usually carried out on crop experimental plots with different treatments in order to determine the level of some factor, such as disease or pest infestation and damage, which are scored for incidence or severity using a pre-determined range of scores. Real data collected in the form of scores on experimental fields are usually non-precise. This non-precision may be due to the scorer's inconsistency and judgmental error. It may also be due to the apparent interdependency of the scores, since a scorer will naturally compare the score of previous plots in order to determine the score of the …