Statistics and Probability Commons^™

A Sensitivity Analysis Of Circular Error Probable Approximation Techniques, Peter Puhek

Theses and Dissertations

Several algebraic CEP estimates models were examined in this study. Each assumes that the crossrange and downrange miss distances of the sample data follow a bivariate normal distribution. The analysis determined the sensitivities of these models to changes in the parameters of sample size, bias, correlation, and ellipticity. The accuracy of each model is expressed in terms of relative error, and the parameter regions in which a certain method dominated as the most accurate were noted. In general, it was found that bias was the most significant parameter in determining the best CEP method. A simple method, based on the …

Transformation Of Combat Data In Support Of Battle Trace, Hyoung-Kyu Choi

Theses and Dissertations

The purpose of this study was to find an appropriate way of characterizing battle data as a function of time. This study was initially designed to remove the numerical instability problem cited in Barr's battle trace methodology as suggested by TRAC-MTRY. The research focused on the instability problem and identifying/recommending a technique that improved the efficiency of computation, and enhanced an analyst's ability to meaningfully interpret the battle trace. Two Lanchester's Square Law based methodologies are introduced and analyzed. The results of this analysis indicate that the battle trace of a constant value generated by Lanchester's Square Law integration seemed …

Confidence Interval Estimation For Output Of Discrete-Event Simulations Using The Kalman Filter, Randall B. Howard

Theses and Dissertations

Discrete-event simulation is computer modeling of stochastic, dynamic systems. The Kalman filter is a Bayesian stochastic estimation algorithm. Because of the correlated nature of simulation output, it is difficult to apply the methods of classical statistics directly when constructing confidence intervals of discrete-event simulation parameters. Through the determination of a dynamics equation and application of the Kalman filter to simulation output data, three new confidence interval construction techniques have been developed. One technique obtains an estimate of the mean value and its associated variance from an estimated Kalman filter. The second technique utilizes Multiple Model Adaptive Estimation (MMAE) techniques to …

Book Review, Thomas G. Field Jr.

RISK: Health, Safety & Environment (1990-2002)

Review of the following book: THOMAS GILOVICH, How WE KNOW WHAT ISN'T SO: THE FALLIABILITY OF REASON IN EVERYDAY LIFE. (The Free Press 1991) [216 pp.] Index, notes. CIP: 90-26727; ISBN: 0-02-911705-4. [Cloth $19.95. 866 Third Ave. New York, NY 10022.]

Multilayer Perceptrons For Classification, Lisa M. Belue

Theses and Dissertations

Techniques for training, testing, and validating multilayer perceptrons are thoroughly examined. Results obtained using perceptrons are compared and contrasted with two multivariate discriminant analysis techniques- logistic regression and k neighbor. Methods for determining significant input features are investigated and a procedure for examining the confidence to place in the significance of these features is developed. Procedures to evaluate the applicability of high-order feature inputs are examined. These methods and procedures are applied to two very different applications. The first application concerns the prediction of Air Force pilot retention/separation rates for input to force projection models. The second application concerns the …

Boundedness And Periodic Solutions In Infinite Delay Systems, Roger H. Hering

Mathematics and Statistics Faculty Research & Creative Works

Liapunov methods are used to give conditions ensuring that solutions of infinite delay equations are uniformly bounded and uniformly ultimately bounded with respect to unbounded (Cg) initial function spaces; and the connection to proving existence of periodic solutions is examined. Several examples illustrate the application of these results, especially to integrodifferential equations. © 1992.

Fixed Point Theorems For D-Complete Topological Spaces I, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These include d-complete symmetric (semi-metric) spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality. © 1992, Hindawi Publishing Corporation. All rights reserved.

Prediction Intervals, Based On Ranges And Waiting Times, For An Exponential Distribution, Laura Colangelo, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

This article contains two prediction intervals applicable to a 2-parameter as well as a 1-parameter exponential distribution. One can be used to predict a future sample range on the basis of an observed sample range. Appropriate prediction factors are tabulated. The other can be used to predict a waiting time between two future successive failures on the basis of an observed waiting time between two previous successive failures. © 1992 IEEE

Reply To Valverde, Paul B. Thompson

RISK: Health, Safety & Environment (1990-2002)

Professor Thompson responds to Valverde's argument, in the last issue, that his approach to Risk puts too much emphasis on the distinction between Risk subjectivism and Risk objectivism. In doing so, he asserts, inter alia, that anchoring Risk judgments in a probabilistic framework does not go far enough in rejecting reigning Risk-analysis notions of "real Risk."

Formation Of Clusters And Resolution Of Ordinal Attributes In Id3 Classification Trees, Chaman Sabharwal, Keith R. Hacke, Daniel C. St. Clair

Computer Science Faculty Research & Creative Works

Many learning systems have been designed to construct classification trees from a set of training examples. One of the most widely used approaches for constructing decision trees is the ID3 algorithm [Quinlan 1986]. Decision trees are ill-suited to handle attributes with ordinal values. Problems arise when a node representing an ordinal attribute has a branch for each value of the ordinal attribute in the training set. This is generally infeasible when the set of ordinal values is very large. Past approaches have sought to cluster large sets of ordinal values before the classification tree is constructed [Quinlan 1986; Lebowitz 1985; …

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

The Statistics Of Lotteries, Matthew Thomas Bremer

Honors Theses, 1963-2015

This project begins with the analysis of several existing lotteries in the state of Minnesota. The raw data of these lotteries are used to calculate the expected values of certain random variables in an effort to describe and compare the lotteries mathematically. Next, the different criteria that contribute to a successful lottery are described and brought together. Finally, via mathematical modeling and computer simulation, a new lottery proposal is presented with the claim that it is superior to existing lotteries from an administrative standpoint.

Boundary Velocity Control Of Incompressible-Flow With An Application To Viscous Drag Reduction, Max D. Gunzberger, Lisheng Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

An optimal boundary control problem for the Navier-Stokes equations is presented. The control is the velocity on the boundary, which is constrained to lie in a closed, convex subset of H^1/2 of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in all application to viscous drag reduction.

Uniqueness Of Radial Solutions Of Semilinear Elliptic Equations, Man Kam Kwong, Yi Li

Mathematics and Statistics Faculty Publications

E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one finite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coefficients.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

The main purpose of this paper is to prove Theorems 1 and 2 of the preceding paper, Part I, together with their extensions and related symmetry results. To make this part essentially self-contained, we shall apply the method developed in Section 2 to equations with radial symmetry. Combining the asymptotic behavior and the "moving plane" technique, we are then able to obtain the desired results.

Missing Data In Repeated Measurement Studies, Kejian Niu

Theses and Dissertations

Repeated measurement data or longitudinal data occur often in statistical applications. For example, in a clinical trial comparing the efficacy of a new treatment with that of a standard treatment, rather than measuring the main response variable only once on each patient, or subject, we can take several measurements over time on each subject.

A Repeated measurement study differs from a longitudinal study. The latter generally refers to any study in which one or more response variables are repeatedly measured over time. The former usually imposes some restrictions on the data. One common restriction is that each response variable must …