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Exponentially Weighted Moving Average Charts For Monitoring The Process Generalized Variance, Anna Khamitova
Exponentially Weighted Moving Average Charts For Monitoring The Process Generalized Variance, Anna Khamitova
Electronic Theses and Dissertations
The exponentially weighted moving average chart based on the sample generalized variance is studied under the independent multivariate normal model for the vector of quality measurements. The performance of the chart is based on an analysis of the chart's initial and steady-state run length distributions. The three methods that are commonly used to determinate run length distribution, simulation, the integral equation method, and the Markov chain approximation are discussed. The integral equation and Markov chain approaches are analytical methods that require a nu- merical method for determining the probability density and cumulative distribution functions describing the distribution of the sample …
Comparing K Population Means With No Assumption About The Variances, Tony Yaacoub
Comparing K Population Means With No Assumption About The Variances, Tony Yaacoub
Electronic Theses and Dissertations
In the analysis of most statistically designed experiments, it is common to assume equal variances along with the assumptions that the sample measurements are independent and normally distributed. Under these three assumptions, a likelihood ratio test is used to test for the difference in population means. Typically, the assumption of independence can be justified based on the sampling method used by the researcher. The likelihood ratio test is robust to the assumption of normality. However, the equality of variances is often difficult to justify. It has been found that the assumption of equal variances cannot be made even after transforming …
Polymorphic Data Modeling, Steven R. Benson
Polymorphic Data Modeling, Steven R. Benson
Electronic Theses and Dissertations
There are currently no data modeling standards for modeling NoSQL document store databases. This work proposes a standard to fill the void. The proposed standard is based on our new data modeling pattern named The Polymorphic Table Pattern. The pattern embraces the “schemaless” nature of document store NoSQL while allowing the data modeler to use his or her existing skillsets. The concepts of our proposed modeling have been demonstrated against MongoDB.
A Constructive Proof Of The Borel-Weil Theorem For Classical Groups, Kostiantyn Timchenko
A Constructive Proof Of The Borel-Weil Theorem For Classical Groups, Kostiantyn Timchenko
Electronic Theses and Dissertations
The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (``Theorem of the Highest Weight''). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\lambda$, for each dominant integral form $\lambda$ on the Lie algebra of a maximal torus of $G$.
Statistical Analysis Of Unreplicated Factorial Designs Using Contrasts, Meixi Yang
Statistical Analysis Of Unreplicated Factorial Designs Using Contrasts, Meixi Yang
Electronic Theses and Dissertations
Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, …
Generalized Weibull And Inverse Weibull Distributions With Applications, Valeriia Sherina
Generalized Weibull And Inverse Weibull Distributions With Applications, Valeriia Sherina
Electronic Theses and Dissertations
In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included …
Generalized Classes Of Distributions With Applications To Income And Lifetime Data, Shujiao Huang
Generalized Classes Of Distributions With Applications To Income And Lifetime Data, Shujiao Huang
Electronic Theses and Dissertations
In this thesis, new classes of distributions namely: exponentiated Kumaraswamy-Dagum (EKD), Log-exponentiated Kumaraswamy-Dagum (Log-EKD), McDonald Log-logistic (McLLog) and Gamma-Dagum (GD) distributions are presented. A thorough and comprehensive investigation of these classes of distributions is conducted. Mathematical properties of these classes of distributions including series expansion, hazard and reverse hazard functions, moments, generating functions, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics, moments of order statistics and entropies are presented. Estimation of parameters of these distributions via maximum likelihood technique, Fisher information and asymptotic confidence intervals are given. Maximum likelihood estimation of the parameters of the exponentiated …
Selection Of Step Size For Total Variation Minimization In Ct, Anna N. Yeboah
Selection Of Step Size For Total Variation Minimization In Ct, Anna N. Yeboah
Electronic Theses and Dissertations
Medical image reconstruction by total variation minimization is a newly developed area in computed tomography (CT). In compressed sensing literature, it hasbeen shown that signals with sparse representations in an orthonormal basis may be reconstructed via l1-minimization. Furthermore, if an image can be approximately modeled to be piecewise constant, then its gradient is sparse. The application of l1-minimization to a sparse gradient, known as total variation minimization, may then be used to recover the image. In this paper, the steepest descent method is employed to update the approximation of the image. We propose a way to estimate an optimal step …
Generating Surfaces Of Variable Eccentricity Within A Ray Tracer, Joshua A. Smith
Generating Surfaces Of Variable Eccentricity Within A Ray Tracer, Joshua A. Smith
Electronic Theses and Dissertations
Polynomial surfaces used in ray tracing have recently been improved upon allowing for three dimensional applications. Among these are surfaces that have a varying eccentricity. This paper will discuss a method for finding real roots of polynomials [allowing us to create these surfaces]. First, we will give the reader a basic comprehension of the workings of a ray tracer, a general understanding of three dimensional polynomial surfaces, how this newly implemented root finder functions, and how these concepts enable us to create surfaces of variable eccentricity. Then, examples will be provided to demonstrate the capabilities of the program.
Precise Partitions Of Large Graphs, Pouria Salehi Nowbandegani
Precise Partitions Of Large Graphs, Pouria Salehi Nowbandegani
Electronic Theses and Dissertations
First by using an easy application of the Regularity Lemma, we extend some known results about cycles of many lengths to include a specified edge on the cycles. The results in this chapter will help us in rest of this thesis. In 2000, Enomoto and Ota posed a conjecture on the existence of path decomposition of graphs with fixed start vertices and fixed lengths. We prove this conjecture when |G| is large. Our proof uses the Regularity Lemma along with several extremal lemmas, concluding with an absorbing argument to retrieve misbehaving vertices. Furthermore, sharp minimum degree and degree sum conditions …
An Investigation Of Sensitivity Of An F Test In Locating Change Points In Linear Regression, Jing Sun
An Investigation Of Sensitivity Of An F Test In Locating Change Points In Linear Regression, Jing Sun
Electronic Theses and Dissertations
Change point is a statistic phenomenon, which has many direct applications in climatology, bioinformatics, finance, oceanography and medical imaging. In this thesis, we investigate the sensitivity of the F-test for detecting change points in linear regression, using a two-phase linear regression model. it offers an effective method to detect "undocumented" change points using a form of an F-test. Using simulated data, we explore its sensitivity and accuracy with respect t different parameters in the model.
Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva
Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva
Electronic Theses and Dissertations
Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.
Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford
Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford
Electronic Theses and Dissertations
Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …
Elements Of Convergence Approach Theory, William D. Trott
Elements Of Convergence Approach Theory, William D. Trott
Electronic Theses and Dissertations
We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.
Adaptive State Feedback Control Of Lorenz Systems To Its Non-Trivial Equilibrium, Anh V. Tran
Adaptive State Feedback Control Of Lorenz Systems To Its Non-Trivial Equilibrium, Anh V. Tran
Electronic Theses and Dissertations
The complex Lorenz system is a simplified nonlinear dynamical system, which is derived from the Navier-Stokes equations that govern a closed thermal convection loop. The Lorenz system is chaotic for large Rayleigh number. In this chaotic regime, we implement a linear state feedback controller to stabilize the state trajectory at its original nontrivial equilibrium. The state variable for feedback is easily measurable. The system is proved to be globally asymptotically stable with a optimal feedback gain. The stability bound is improved over the previous result. We also established globally stability of the adaptively control system, where the system parameters are …