Statistics and Probability Commons^™

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

On Conformal Scalar Curvature Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

Cyclic Operators, Commutators, And Absolutely Continuous Measures, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

Commutator equations are used to study the relationship between the tridiagonal matrix structure of an unbounded cyclic selfadjoint operator and its spectrum. Sufficient conditions are given for absolute continuity. Results are related to the study of systems of orthogonal polyomials for which the measure of orthogonality is supported on an unbounded subset of the real line.

Large Deviation Local Limit Theorems For Ratio Statistics, Sanjeev V. Sabnis

Mathematics & Statistics Theses & Dissertations

Let {T„, n > 1} be an arbitrary sequence of non-lattice random variables and {S_n, n > 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø_1n and Ø_2n be the moment genereating functions of {Tn, n > 1} and { S_n,n > 1} respectively. Let {a_n} be a sequence of real numbers such that a_n —»• oo.

Nonparametric Confidence Intervals For The Reliability Of Real Systems Calculated From Component Data, Jean Spooner

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A methodology which calculates a point estimate and confidence intervals for system reliability directly from component failure data is proposed and evaluated. This is a nonparametric approach which does not require the component time to failures to follow a known reliability distribution.

The proposed methods have similar accuracy to the traditional parametric approaches, can be used when the distribution of component reliability is unknown or there is a limited amount of sample component data, are simpler to compute, and use less computer resources. Depuy et al. (1982) studied several parametric approaches to calculating confidence intervals on system reliability. The test …

A Test For Determining An Appropriate Model For Accelerated Life Data, Yuan-Who Chen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis was to evaluate a method for testing the appropriateness of accelerated life model. This method is based upon a polynomial approximation. The parameters are estimated and used for testing the appropriateness of the model.

An example illustrates the polynomial method. Real data are applied for this method. Comparison with another method demonstrates that the polynomial method is much simpler and has comparable accuracy.

A Comparison Of Rank And Bootstrap Procedures For Completely Randomized Designs With Jittering, Feng-Ling Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper discusses results of a computer simulation to investigate the effect of jittering to simulate measurement error. In addition, the classical F ratio, the bootstrap F and the F for ranked data are compared. Empirical powers and p-values suggest the bootstrap is a good and robust procedure and the rank procedure seems to be too liberal when compared to the classical F ratio.

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

Orthogonal Polynomials, Measures And Recurrence Relations, Joanne Dombrowski, Paul Nevai

Mathematics and Statistics Faculty Publications

Properties of measures associated with orthogonal polynomials are investigated in terms of the coefficients of the three term recurrence formula satisfied by the orthogonal polynomials.

An Analysis Of Public Attitudes Toward The Insanity Defense, Valerie P. Hans

Cornell Law Faculty Publications

Results from a public opinion survey of knowledge, attitudes, and support for the insanity defense indicate that people dislike the insanity defense for both retributive and utilitarian reasons: they want insane law-breakers punished, and they believe that insanity defense procedures fail to protect the public. However, people vastly overestimate the use and success of the insanity plea. Several attitudinal and demographic variables that other researchers have found to be associated with people's support for the death penalty and perceptions of criminal sentencing are also related to support for the insanity defense. Implications for public policy are discussed.

L(P) Estimates For Maximal Functions And Hilbert-Transforms Along Flat Convex Curves In R(2), Hasse Carlsson, Michael Christ, Antonio Cordoba, Javier Duoandikoetxea, Jose L. Rudio De Francia, Jim Vance, Stephen Wainger, David Weinberg

Mathematics and Statistics Faculty Publications

No abstract provided.

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

Computer Program Generation Of Extreme Value Distribution Data, Stephen (Wan-Tsing) Lei

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The application of the Monte Carlo method on the estimation in Gumbel extreme value distribution was studied. The Gumbel extreme value distribution is used to estimate the flood flow of specific return period for the design of flood mitigation project. This paper is a programming effort (1) to estimate the parameters of Gumbel distribution using the observed data and (2) to provide a random variate generating subroutine to generate random samples and order statistics of a Gumbel distribution random variable. The mean squared error is used to measure the accuracy of the estimation method. Finally, an example of the use …

Data Analysis Using Experimental Design Model Factorial Analysis Of Variance/Covariance (Dmaovc.Bas), Wesley E. Newton

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

DMAOVC.BAS is a computer program written in the compiler version of microsoft basic which performs factorial analysis of variance/covariance with expected mean squares. The program accommodates factorial and other hierarchical experimental designs with balanced sets of data. The program is writ ten for use on most modest sized microprocessors, in which the compiler is available. The program is parameter file driven where the parameter file consists of the response variable structure, the experimental design model expressed in a similar structure as seen in most textbooks, information concerning the factors (i.e. fixed or random, and the number of levels), and necessary …

Statistical Calibration Theory, James John Mckeon

Mathematics & Statistics Theses & Dissertations

A calibration method substitutes for measurements, X(,i), that are accurate but impractical or costly, a set of measurements, Y(,i), that are less accurate but simpler or less costly. There are two general types of calibration methods. The classical approach in which once the calibration sample is drawn, the estimates of the X values for a given unit is found without any consideration of the distribution of X values for the other units to be measured. This corresponds best to the literal meaning of the word "calibration". Maximum likelihood estimation is the statistical formulation of the classical approach.

The second approach …

Ua56/1 Fact Book, Wku Institutional Research

WKU Administration Documents

Statistical and demographic profile of WKU.

Cramer Type Large Deviations For Generalized Rank Statistics, Munsup Seoh, Stegan S. Ralescu, Madan L. Puri

Mathematics and Statistics Faculty Publications

A Cramer type large deviation theorem is proved under alternatives as well as under hypothesis for the generalized linear rank statistic which includes as special cases (unsigned) linear rank statistics, signed linear rank statistics, linear combination of functions of order statistics, and a rank combinatorial statistic.

Monte Carlo Simulation Of The Game Of Twenty-One, Douglas E. Loer

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this paper is to demonstrate the application of computer simulation to the game of Twenty-One to predict a player's expected return from the game. Twenty-One has traditionally been one of the most popular casino games and has attracted much effort to accurately estimate the house's true advantage. Probability theory has been tried, but the thousands of different combinations of cards possible in all hands throughout the entire pack make it practically impossible to apply probability theory without overlooking some possibilities. For this reason, Twenty-One is a perfect candidate for simulation. By blocking several simulations, normal theory can …

Unbalanced Analysis Of Variance Comparing Standard And Proposed Approximation Techniques For Estimating The Variance Components, James P. Pugsley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper considers the estimation of the components of variation for a two-factor unbalanced nested design and compares standard techniques with proposed approximation procedures. Current procedures are complicated and assume the unbalanced sample size to be fixed. This paper tests some simpler techniques, assuming sample sizes are random variables. Monte Carlo techniques were used to generate data for testing of these new procedures.

Perturbation Of Periodic Boundary-Conditions, Larry Turyn

Mathematics and Statistics Faculty Publications

We consider perturbations of the problem (*) - x'' + bx = lambda ax, x(0) - x(1) = 0 = x'(0) - x'(1) both by changes of the boundary conditions and by addition of nonlinear terms. We assume that at lambda = lambda 0 there are two linearly independent solutions of the unperturbed problem (*) and that a(dot) is bounded away from zero. When only the boundary conditions are perturbed either the Hill’s discriminant or the method of Lyapunov–Schmidt reduces the problem to 0 = det ((lambda - lambda 0)A - epsilon …

Correction Of Bias In Estimating Autocovariance Function, Len-Hong Wu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis was to evaluate a method for reducing the bias of estimation for autocovariance estimators. Two methods are compared, one is the standard method and the other is an adjustment method. The Monte Carlo method is used within comparison.

The bias and the mean squared error of the estimated autocovariance is computed for several time series models and two variations of the adjustment method of estimation. The results indicate some improvement in bias and mean squared error for the new method.

An Analysis Of The Median Polish Procedure, Patricia M. Burgess, David L. Farnsworth

Articles

The effect of the median polish procedure on artificial data having known general characteristics, disturbances, and random elements is examined. Monte Carlo experiments were designed for this purpose. The behavior of the fits, residuals, and various accompanying statistics are determined under special controlled conditions. Then, the procedure is applied to selected data sets from the literature utilizing the findings of this study.

The Use Of Contingency Table Analysis As A Robust Technique For Analysis Of Variance, Mei-Eing Chiu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to compare Analysis of Variance with Contingency Table Analysis when the data being analyzed do not satisfy Analysis of Variance assumptions. The criteria for comparison are the powers of the Standard variance-ratio and the Chi-square test.

The test statistic and powers were obtained by Monte Carlo.

1. Calculate test statistic for each of 100 trials, this process was repeated 12 times. Each time different combination of means and variances were used.

2. Powers were obtained for each of 12 combinations of means and variances.

Whether Analysis of Variance or Contingency Table Analysis is a …

Least Squares Estimation Of The Pareto Type I And Ii Distribution, Ching-Hua Chien

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The estimation of the Pareto distribution can be computationally expensive and the method is badly biased. In this work, an improved Least Squares derivation is used and the estimation will be less biased. Numerical examples and figures are provided so that one may observe the solution more clearly. Furthermore, by varying the different methods of estimation, a comparing of the estimators of the parameters is given. The improved Least Squares derivation is confidently employed for it is economic and efficient.

Parameter Estimation In Nonstationary M/M/S Queueing Models, Pensri Vajanaphanich

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

If either the arrival rate or the service rate in an M/M/S queue exhibit variability over time, then no steady state solution is available for examining the system behavior. The arrival and service rates can be represented through Fourier series approximations. This permits numerical approximation of the system characteristics over time.

An example of an M/M/S representation of the operations of emergency treatment at Logan Regional hospital is presented. It requires numerical integration of the differential equation for L(t), the expected number of customers in the system at time t.

Linear Regression Of The Poisson Mean, Duane Steven Brown

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis was to compare two estimation procedures, the method of least squares and the method of maximum likelihood, on sample data obtained from a Poisson distribution. Point estimates of the slope and intercept of the regression line and point estimates of the mean squared error for both the slope and intercept were obtained. It is shown that least squares, the preferred method due to its simplicity, does yield results as good as maximum likelihood.

Also, confidence intervals were computed by Monte Carlo techniques and then were tested for accuracy. For the method of least squares, confidence …

Evidence Of Intrinsic Double Acceptor In Gaas, Phil Won Yu, W. C. Mithel, M. G. Mier, S. S. Li, Weizhen Wang

Mathematics and Statistics Faculty Publications

Acceptors present in undoped p‐type conducting GaAs have been studied with photoluminescence, temperature‐dependent Hall measurements, deep level transient spectroscopy, and spark source mass spectrometry. It is shown that p‐type conduction is due to presence of the shallow acceptor C_As and the cation antisite double acceptor Ga_As. The first and second ionization energies determined for Ga_As are 77 and 230 meV from the valence‐band edge.

Nonparametric Analysis Of Right Censored Data With Multiple Comparisons, Hwei-Weng Shih

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This report demonstrates the use of a computer program written in FORTRAN for the Burroughs B6800 computer at Utah State University to perform Breslow's (1970) generalization of the Kruskal-Wallis test for right censored data. A pairwise multiple comparison procedure using Bonferroni's inequality is also introduced and demonstrated. Comparisons are also made with a parametric F test and the original Kruskal-Wallis test. Application of these techniques to two data sets indicate that there is little difference among the procedures with the F test being slightly more liberal (too many differences) and the Kruskal-Wallis test corrected for ties being slightly more conservative …

An Analysis Of The Impact Of The 55 Mph Speed Limit, David L. Farnsworth, Kenneth Mathis, Janet Herbert

Articles

In January 1974 the speed limit on the New York State Thruway was set at 55 mph for all vehicles. This paper examines the effect of that action on Thruway fatality rates. The exact number of total miles driven is known for this toil road. Hence, death rates are based upon precise information. Since seven years have elapsed during the post-treatment period, 1974-1980, longer trends can be investigated. The death rate is modeled and intervention analysis performed. Using a variety of forecasting techniques, the pre-treatment fatality rates are used to project rates through the post-treatment period. In this way, the …

Explanation Of The Fast Fourier Transform And Some Applications, Alan Kazuo Endo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This report describes the Fast Fourier Transform and some of its applications. It describes the continuous Fourier transform and some of its properties. Finally, it describes the Fast Fourier Transform and its applications to hurricane risk analysis, ocean wave analysis, and hydrology.