STAT Statistics

STAT   5130G   Sampling and Survey Methods

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An introduction to the design and analysis of sample surveys suitable for students in business, social sciences, and biological sciences in addition to the mathematical sciences. Comparison of simple random sampling, stratified, systemic, cluster and multistage sampling. Emphasis on appropriate sample type and estimation of parameters. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Cross Listing(s): STAT   5130.

STAT   5330G   Introduction to Mathematical Statistics

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

An introductory course intended to present a solid foundation in statistical theory, and, at the same time, to provide an indication of the relevance and importance of the theory in solving practical problems in the real world. Topics include, moments and moment-generating functions, point and interval estimation, test of statistical hypothesis, contingency tables and goodness-of-fit, nonparametric methods, and introduction to linear models. This course covers part of the material outlined in the Society of Actuaries' course 110. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Prerequisite(s): A minimum grade of "C" in MATH   3337.

Cross Listing(s): STAT   5330.

STAT   5531G   Statistical Methods I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

This is the first of a two course sequence in applied statistics. The material covered will provide an introduction to statistical concepts and terminology while focusing on descriptive and inferential methods of data analysis. Topics include descriptive statistics, parameter estimation, tests of significance, confidence intervals, analysis of variance, simple linear regression and correlation, and resampling methods including bootstrapping. Both parametric and nonparametric methods are presented for the analysis of central tendency, variability, proportions and categorical data. Graduate students will be required to complete advanced level assignments in an area beyond the scope of the undergraduate requirements that demonstrates a higher level of mastery in the subject matter with additional required deliverables representative of graduate level work, as determined by the instructor.

Prerequisite(s): A minimum grade of "C" in MATH   3337.

Cross Listing(s): STAT   5531.

STAT   5532G   Statistical Methods II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

This is the second of a two course sequence in applied statistics. The material covered will provide an introduction to the ideas of linear models and experimental design while focusing on methods of data analysis using regression and analysis of variance. Topics include multiple regression analysis, analysis of variance with multiple classification, analysis of covariance, repeated measures analysis of variance, multiple comparison techniques, and diagnostic procedures and transformations. Suitable for students in business administration, economics, and the social, health and biological sciences. Graduate students will be given an extra assignment determined by the instructor that undergraduates will not be required to do.

Cross Listing(s): STAT   5532.

STAT   7090   Selected Topics in Statistics

1-3 Credit Hours.   1-3 Lecture Hours.   0-2 Lab Hours.

Selected study in a selected area of Statistics.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7130   Applied Multivariate Statistical Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Estimating and inference from the multivariate normal distribution, Hotelling's T 2, multivariate analysis of variance, multivariate regression, multivariate experimental design, principle component analysis, factor analysis, discriminate analysis and cluster analysis.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7132   Applied Nonparametric Statistics

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Review of probability and statistical inference; binomial, quantile and sign tests; contingency tables; methods based on ranks.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7134   Applied Regression Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Simple and multiple linear regression, model selection, residual analysis, influence diagnostics, transformation of data to fit assumptions, multicollinearity and an introduction to nonlinear regression.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7135   Analysis of Discrete Data

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

The study of discrete univariate and multivariate distributions and generating functions, two-way and higher dimensional contingency tables, chi-squared and other goodness-of-fit tests, Cochran-Mantel-Hanzel procedure, binary and multinomial response models, log-linear models, theoretical foundations for the generalized linear models, mixed generalized linear models, longitudinal and spatial data analysis.

Prerequisite(s): STAT   7331 and STAT   5531, with a minimum grade of "C".

STAT   7231   Design of Experiments I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Various statistically designed experiments are introduced including randomized blocks designs, Latin squares, incomplete block designs, factorial and fractional factorial designs with and without confounding and nested designs.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7232   Design of Experiments II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Response surface methodology is introduced. First- and second-order models and designs are studied which includes determining optimum conditions and methods of estimating response surfaces. Multiresponse experiments, nonlinear response surface models, and mixture designs are also studied.

Prerequisite(s): STAT   7231.

STAT   7234   Statistical Process Control

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Philosophy of statistical process control is studied along with SPC techniques of control charts, process-capability, designed experiments and acceptance sampling.

Prerequisite(s): STAT   5531 or STAT   5531G.

STAT   7331   Mathematical Statistics I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Random variables, density functions, mathematical expectation, discrete and continuous distributions, moments and moment-generating functions and limiting distributions.

Prerequisite(s): MATH   2242 and MATH   3337.

STAT   7332   Mathematical Statistics II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Rigorous introduction/development of interval estimation, test of significance, comparison of “k” means, randomized block design, multiple comparison procedures, nonparametric test and linear regression. The general linear model will be introduced.

Prerequisite(s): STAT   7331.

STAT   7430   Actuarial Mathematics

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Survival distributions and life tables, life insurance, life annuities, net premiums, multiple life functions, multiple decrement models, valuation theory for pension plans, collective risk models, population theory and theory of pension funding.

Prerequisite(s): STAT   7331.

STAT   7432   Applied Stochastic Processes

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Poisson process, renewal theory, Markov chains, Brownian motion, random walks and Martingales and stochastic order relations.

Prerequisite(s): STAT   7331 with a minimum grade of "C".

STAT   7434   Applied Time Series Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Basic ideas of stochastic model building techniques with applications are discussed. Properties of the autocorrelation function and the spectrum of stationary processes are investigated. Models studied include the linear stationary ARMA and linear non-stationary ARIMA models along with forecasting models.

Prerequisite(s): STAT   7331.

STAT   7436   Reliability Analysis

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Probabilistic models for the reliability of coherent systems, statistical models for lifetimes of components and repairable systems, including the nonhomogeneous Poisson process, reliability estimation and prediction, MIL standards and accelerated life testing.

Prerequisite(s): STAT   7331.

STAT   7530   Statistical Computing I

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Basic computer organization and computer arithmetic are investigated. Programming languages and statistical software packages are explored. Methods for approximating cumulative distribution function and percentage points of a probability distribution are studied including nonparametric procedures. Multiple comparison procedures are also examined. Random number generation and statistical tests for testing random number generators are explored.

Prerequisite(s): STAT   7331.

STAT   7532   Statistical Computing II

3 Credit Hours.   3 Lecture Hours.   0 Lab Hours.

Various computational methods in linear algebra as applied to such statistical methods as multiple linear regression, designed experiments, multivariate analysis and the general linear model. Further topics include computational methods for unconstrained optimization, nonlinear regression and model fitting based on criteria other than least squares.

Prerequisite(s): STAT   5532 or STAT   5532G, and STAT   7331.

STAT   7610   Gradute Seminar

1 Credit Hour.   1 Lecture Hour.   0 Lab Hours.

Students will research topics related to their major/concentration, under supervision of one or more faculty members. Each student will present results on topics of interest to the class on new developments in mathematical sciences, or on his/her research project. Faculty members also may present lectures for the benefit of the students. Course may be repeated up to a maximum of 3 credit hours to be counted toward the M.S. in Mathematics.

Cross Listing(s): MATH   7610.

STAT   7890   Directed Study in Statistics

1-3 Credit Hours.   1-3 Lecture Hours.   0-2 Lab Hours.

Directed study under faculty supervision.

Prerequisite(s): Permission of instructor and Department Chair.

STAT   7895   Research

1-3 Credit Hours.   0 Lecture Hours.   0 Lab Hours.

Graduate students will conduct a program of independent research under the direction of a thesis advisor or an advisory committee on a topic in Statistics. Results of the research will be presented as a thesis in MATH   7999 for partial fulfillment of the requirement of the Master of Science Degree in Mathematics with an emphasis in Statistics.

STAT   7899   Research Project in Statistics

1-6 Credit Hours.   1-6 Lecture Hours.   0-4 Lab Hours.

Research project addressed toward a real world problem.

Prerequisite(s): Permission of project advisor and Department Chair required.