Modification of the Statistics Program Courses
and Study Plans
Prepared by
The Accreditation Committee of the Statistics Program
Dr. Ayman Baklizi,
Program Director and Chair of the Accreditation Committee
Dr. Adil Eltayeb (Member)
Dr. Ameen Alawneh (Member)
June 2010
1
Table of Contents
1. Introduction………………………………………………………………….3
2. The Mission, Program Objectives and Learning Outcomes…………………5
3. Other General Program related Issues……………………………………….8
4. The Modified Study Plan for the Major ……………………………………10
5. Brief Course Descriptions..............................................................................15
6. The Minor in Statistics………………………..…………………………….25
7. The Course Math 251“Mathematics for Statistics”………………………....28
8. Course Syllabi.................................................................................................31
2
Introduction
3
Introduction
The Department of Mathematics, Statistics, and Physics at QU is currently engaged in an intensive
preparation for the specialized accreditation of its undergraduate statistics program. As a part of the
accreditation process, a team of assessors from the Royal Statistical Society (RSS) conducted a
comprehensive evaluation visit to the department from 2 to 6 March 2008 to consider its
application for the accreditation. The visiting team toured the department and the university, met
with the program staff and held separate open meeting for a group of undergraduate students. On
the basis of their observations and after analyzing relevant documents provided by the department,
the team prepared and submitted an assessment report. The assessment report gives a rigorous
academic review of the program in the areas of curriculum, management, support facilities and
student welfare. The RSS report, also, raised some critical issues regarding the program design and
structure, and included several recommendations and suggestions for enhancement.
The present document is developed in response to the visiting team report. It focuses on the issues
addressed in their assessment report and on the corresponding recommended actions concerning
the curriculum. The modifications include developing new courses, modifying some existing
courses and the necessary changes in prerequisites. Included below are the study plans for the
major in Statistics-Minor in Business or Minor in computer science and the study plan for the
Minor in Statistics. The course short syllabi for the courses are also included.
4
The Program mission,
objectives and learning
outcomes
5
The Mission
The mission of the Statistics Program at Qatar University is to provide quality education
with student-centered learning environment to produce high level graduates. The program
aims at blending theory with practice by involving the students with interactive learning
processes including research projects with real situations covering data collection and
description to data analysis using the various modern day technologies and
communicating the results precisely and effectively. The program allows the graduates to
think as problem solvers with innovation and creativity and they will be equipped with the
skills and knowledge to potentially provide consulting services to the various academic
and professional sectors in the Qatari society.
Program Objectives
1-
Gain knowledge in the principles of statistics and its application to the other related
fields of applications.
2-
Build Strong theoretical background for the statistical techniques used.
3-
Have a good understanding of the statistical principles and methods necessary to
collect data including experimental design and statistical surveys.
4-
Have a good training in statistical computing necessary to conduct different kinds of
data analysis.
5-
Gain the ability to provide sound "statistical consultation" to users of statistics in the
different disciplines.
6-
Acquire the ability to communicate effectively orally and in writing to undertake
statistical tasks.
7-
Promote critical learning skills and enabling students to be lifelong learners
Student Learning Outcomes
Students will be able to
1. Collect and give advice on how to collect data that conform with the statistical principles of
data collection.
2. Design or give advise on to design surveys and experiments to obtain high quality data.
3. Describe various types of data numerically and graphically.
4. Analyze the various types of data that arise in the various types of scientific investigations.
5. Use effectively the statistical packages to conduct the various types of statistical tasks.
6. Write and present professional statistical reports and communicate effectively with the
various users of statistics.
7. Demonstrate the theoretical basis of the statistical methods used in a given situation
6
Matrix of Compulsory Courses Mapped to Program
Learning Outcomes
211 221 101 231 332 361 371 499
Student Learning Outcomes
312 322 102 333
481
1. Collect and give advice on how to collect data that
conform with the statistical principles of data
collection
2. Design or give advise on to design surveys and
experiments to obtain high quality data
*
3. Describe various types of data numerically and
graphically
*
*
*
*
*
*
*
*
*
*
*
*
4. Analyze the various types of data that arise in the
various types of scientific investigations
5. Use effectively the statistical packages to conduct
the various types of statistical tasks.
6. Write and present professional statistical reports
and communicate effectively with the various users of
statistics
7. Demonstrate the theoretical basis of the statistical
methods used in a given situation
*
*
*
*
*
*
*
*
*
*
7
Other General Program
Related Issues
8
During the last months, considerable attention was paid to the marketing of the Statistics Program. Several
steps were undertaken to communicate with statistics users outside the university. As for prospective students,
presently in schools or in the foundation program, an action plan was set that includes participation in and
organizing open days. This is to introduce them to the statistics program and the possible opportunities for
graduates in statistics. Work on the Statistics Program is currently going on to enhance and improve the content and
presentation of the relevant information for the prospective students.
Qatar Statistical Authority (QSA) is an official governmental body that is responsible of many tasks
including censuses and surveys of various types. This is a place where there is a high demand for Qatari
statisticians. Contacts were began between Statistics Program of Qatar university and QSA to start
cooperation. Some Statistics students will do their graduate projects that are relevant to the QSA needs.
Job opportunities are open their to the extent that they are willing to support statistics students on the
condition of working with them after graduation.
Some activities during the university and college open days were already done. There is an action plan for
the marketing of Statistics that include open days especially for the Statistics program. These are expected
to be done during Spring 2010 semester.
During the last year, some of the Statistics Program members:









Attended the University Open Day for female students on 11/3/2009.
Attended the CAS Open Day for male students on 9/11/2009 at the foundation building.
Attended the CAS Open Day for female students on 11/11/2009 at the foundation building.
Presented PowerPoint slides about the program and employment opportunities in Statistics. Two
Statistics students participated in this event.
Participated in the Statistical Symposium, Qatar Statistical Authority, November 2008
Arranged A scientific trip to the Supreme Council of Education December 2008
Arranged A scientific trip to Qatar Statistic Authority May 2009
Attended the Strategic Qatarization Plan meeting April 2009
Participated together with some the senior students in the High Level Meeting on
Mainstreaming Sectoral Statistical System (QSA) October 2009
Held several meetings as well as in the public presentation highlighting the statistics program
activities.
Other activities include

A student handbook, career booklet together with some posters and guides are currently under
preparation.

Work is started on updating and improving the website of the Statistics Program.

Student’s Club: Dr. Adil Yousif is currently the supervisor. The club produces Monthly newsletter.

Student Advisor: Dr. Mohanad Alkhasawneh is currently the advisor of all Statistics students.


Curriculum Committee: It is formed with three members.
Strategic Plan: A committee for strategic planning is formed in the department and the work was
started with well defined goals, objectives and action plan.
9
The Modified Study
Plan
10
Study Plan
College: Arts and Sciences
Program:
Dept.: Mathematics, Statistics and Physics
Major Statistics – Minor Business
Degree: Bachelor of Science (B. Sc.)
Total credit hours required for graduation: 120 Credit Hours
Program starts on:
Fall Semester
Maximum No. of admitted students: Male
Admitting Criteria :
Foundation Program
Graduation Project:
----------
Practical Training:
----------
Academic Year: 2010-2011
25
Female: 40
General Outline for the Study Plan:
Requirement
Cr. Hrs Required
University Requirements
33
College Requirements
---
Major Compulsives
39
Major Electives
12
Supporting Compulsives
12
The Minor
24
Total
120
11
University Requirements: 33 Credit Hours
Note: The research skills package was removed because some of its courses was covered by the major
Group
Requirement
Total Credit
Hours
Course
ARAB 100 Arabic Language
1
Arabic Language
6
2
English Language
3
Islamic Culture
4
Critical Thinking
3
5
History
3
6
Communications
Skills
3
7
General Knowledge
3
8
Humanities for
science track
6
ARAB 200 Arabic Language II
ENGL 202 English Language I Post Foundation
ENGL 203 English Language II Post Foundation
6
DAWA 111 Islamic Culture
3
Major Compulsive Courses: (39 Credit Hours)
Course No.
Credit Hours
Course Name
Pre-requisite(s):
No. / Name
---
Semester offered
STAT 101
3
Statistics I
Fall
STAT 102
3
Statistics II
STAT 101
STAT 211
3
Introduction to Probability
Math 102 and STAT 101
Fall
STAT 221
3
Mathematical Statistics I
Math 251 and STAT 211
Spring
STAT 231
3
Applied Regression Analysis
STAT 102 and STAT 211
Spring
STAT 312
3
Stochastic Processes
STAT 211 and Math 251
Fall
STAT 322
3
Mathematical Statistics II
STAT 221
Fall
STAT 332
3
Design of Experiments
STAT 102 and STAT 211
Fall
STAT 333
3
Time Series
STAT 231
Spring
STAT 361
3
Sampling Methods
STAT 102 and STAT 211
Spring
STAT 371
3
Statistical Packages
STAT 231
Fall
STAT 481
3
Multivariate Analysis
STAT 322 and Math 231
Fall
STAT 499
3
Graduation Project
Department Approval
Spring
Spring
12
Major Elective Courses: (12 Credit Hours)
Course
No.
Credit
Hours
STAT 241
3
Biostatistics
STAT 102 or STAT 151
STAT 242
3
Demography
STAT 102
Spring
STAT 341
3
Actuarial Statistics I
STAT 102 and STAT 211
Spring
STAT 343
3
Applied Survival Analysis
STAT 102
STAT 344
3
Quality Control
STAT 102 and STAT 211
STAT 372
3
Statistical Simulation
STAT 211
Fall
STAT 381
3
Categorical Data Analysis
STAT 231
Spring
STAT 382
3
Nonparametric Methods
STAT 221
Fall
STAT 434
3
Generalized Linear Models
STAT 322
Fall
STAT 442
3
Actuarial Statistics II
STAT 341
Fall
STAT 445
3
Reliability and Life Testing
STAT 322
Spring
STAT 464
3
Environmental Statistics
STAT 312 and STAT 361
Spring
STAT 482
3
Bayesian Statistics
STAT 322
Fall
STAT 498
3
Special Topics
Department Approval
Fall
Course Name
Pre-requisite(s):No. / Name
Semesters offered
Fall
Fall
Spring
Supporting Compulsive Courses: (12 Credit Hours)
Course No.
Credit Hours
Pre-requisite(s):No. /
Name
Course Name
MATH 101
3
Calculus (1)
---
MATH 102
3
Calculus (2)
MATH 101
MATH 251
3
Mathematics for Statistics
MATH 102
MATH 231
3
Linear Algebra
MATH 102
The Minor (24 Credit Hours)
The students have the following choices for their minor;
a- Minor in Computer Science
b- Minor in Business
c- Minor in Sociology
Important Remarks
 Statistics students are not allowed to take STAT 151, STAT 154 or STAT 350.
 Statistics students with minor in Sociology are not allowed to take SOCI 261.
 Statistics students with minor in Business are not allowed to take STAT 220 or STAT 222.
13
Course Sequencing: Study Plan
First Semester (15 Credit Hours)
Second Semester (15 Credit Hours)
STAT 101
Statistics I
STAT 102
Statistics II
MATH 101
Calculus (1)
MATH 102
Calculus (2)
University Requirement 1
University requirement 4
University Requirement 2
University Requirement 5
University Requirement 3
University Requirement 6
Third Semester (15 Credit Hours)
Fourth Semester (15 Credit Hours)
STAT 211
Introduction to Probability
STAT 221
Mathematical Statistics I
MATH 251
Mathematics for Statistics
STAT 231
Applied Regression Analysis
MATH 231
Linear Algebra
University Requirement 9
University requirement 7
University Requirement 10
University Requirement 8
University Requirement 11
Fifth Semester (15 Credit Hours)
Sixth Semester (15 Credit Hours)
STAT 322
Mathematical Statistics II
STAT 333
Time Series
STAT 371
Statistical Packages
STAT 332
Design of Experiments
STAT 312
Stochastic Processes
STAT 361
Sampling Methods
Minor 1
Minor 3
Minor 2
Minor 4
Seventh Semester (15 Credit Hours)
STAT 481
Multivariate Analysis
Eighth Semester (15 Credit Hours)
STAT 499
Graduation Project
Major Elective 1
Major Elective 3
Major Elective 2
Major Elective 4
Minor 5
Minor 7
Minor 6
Minor 8
14
Brief COURSE
DESCRIPTIONS
15
Course Description:
Course Number: STAT 101
Course Name: Statistics I
Credit Hours: 3 (2+2)
Pre-requisite: None
Semester Offered: Fall
Course Content: Basic concepts, Population.Types of data, Sampling methods, Tables and graphs.
Descriptive Statistics, Basic probability concepts, Random experiment. Sample space, Rules of probability.
Counting techniques. Conditional probability. Independence, Discrete and continuous random variables.
Sampling distributions, The Student-t distribution, F – distribution and Chi-Square distribution, Point
estimation. Confidence intervals for a single population, Testing hypotheses for a single population.
Statistical software like Minitab and Excel are used.
Course Number: STAT 102
Course Name: Statistics II
Credit Hours: 3 (2+2)
Pre-requisite: STAT 101
Semester Offered: Spring
Course Content: Chi-Square Procedures, The Chi-square distribution. Chi-square goodness of fit test.
Contingency tables. Association. Chi-square test for independence. The F-distribution. The completely
randomized design. Multiple comparisons. The randomized block design. The two factor factorial design,
Simple regression equation. Inference about the regression quantities. Nonparametric Statistics, The sign
test and Wilcoxon signed rank test, the Wilcoxon rank sum test. The kruskall-Wallis test. The Friedman
test. The Spearman correlation coefficient. Statistical software like Minitab and Excel are used.
Course Number: STAT 211
Course Name: Introduction to Probability
Credit Hours: 3 (2+2)
Pre-requisite: MATH 102 and STAT 101
Semester Offered: Fall
Course Content : Random experiment. Sample spaces, Events. Axioms and rules of probability. Equally
likely sample spaces. Counting techniques, Conditional probability. Random variables. Expected values.
Moment generating function. Probability generating function, Probability distributions, uniform, Bernoulli,
16
binomial, geometric, negative binomial, Poisson and hypergeometric. exponential, gamma, beta and
normal. Discrete and continuous bivariate random variables. Joint, Marginal and conditional distributions.
Course Number: STAT 221
Course Name: Mathematical Statistics I
Credit Hours: 3 (2+2)
Pre-requisite: STAT 211 and MATH 251
Semester Offered: Spring
Course Content: The Multinomial and multivariate normal distributions. Functions of random variables.
2
Transformation techniques. Sampling Distributions, the t, the  , and the F distributions. The distribution of
a single order statistic. The joint distribution of two order statistics. Distributions of functions of order
statistics. Limit Theorems, Convergence in distribution, Convergence in Probability, Laws of large
numbers. Limiting distributions. The Central limit theorem.
Course Number: STAT 231
Course Name: Applied Regression Analysis
Credit Hours: 3 (2+2)
Pre-requisite: STAT 102 and STAT 211
Semester Offered: Spring
Course Content: Simple Linear Regression; Residual Analysis; Autocorrelation; Multiple Regression;
Parameter Estimation and Testing; Model Selection Procedures; Polynomial Regression; Indicator
Variables; Multicollinearity; Outliers and Influential Observation. Statistical software like Minitab, SPSS and
R are used.
Course Number: STAT 241
Course Name: Biostatistics
Credit Hours: 3 (2+2)
Pre-requisite: STAT 102 or STAT 151
Semester Offered: Fall
Course Content : Methods of Sampling in Medical Studies; Summarizing and Presenting Medical Data;
Demographic Statistics; Survival Analysis; Analysis of Cross Tabulation; Inference for Means; Parametric
and Non-Parametric with applications to medical data; Multiple Linear, Logistic, Poisson and Cox
regression applied to medical data; Sample Size Determination. Statistical software like Minitab and
Excel are used.
17
Course Number: STAT 242
Course Name: Demography
Credit Hours: 3 (2+2)
Pre-requisite: STAT 102
Semester Offered: Spring
Course Contents: Basic Concepts, Meaning of population, Demographic rates. Period rates. Person
years. Growth rate. The concept of cohort. The crude death rate. Age-specific death rates. The Lexis
diagram. Mortality rates. Single-failure indices. The standardized death rate. The standardized mortality
ratio. Life Tables, Multiple Decrement Life Tables, Fertility and Reproduction, Modeling Age Patterns
Course Number: STAT 312
Course Name: Stochastic Processes
Credit Hours: 3 (2+2)
Pre-requisite: STAT 211 and MATH 251
Semester Offered: Fall
Course Content : Elements of Stochastic Processes; Discrete Time Markov Chains; Random Walks;
Branching Processes; Poisson Processes; Birth and Death Processes; Queuing Systems; Renewal
Processes. Basic theory of martingales and Brownian motion. Applications to stochastic financial modeling.
.
Course Number: STAT 322
Course Name: Mathematical Statistics II
Credit Hours: 3 (2+2)
Pre-requisite: STAT 221
Semester Offered: Fall
Course Content: Consistency, Sufficiency, the exponential family of distributions. Completeness
of a family of distributions. Theory of Point Estimation, Criteria for judging point estimators. The
mean squared error and the variance. Unbiasedness, Rao-Blackwell Theorem. Uniformly minimum
variance unbiased estimation. Lower bounds of the variance of unbiased estimators. Information.
Efficiency of an estimator. Maximum likelihood method. Moments method. Least squares method.
Comparisons between the different methods. Interval estimation, Pivotal quantities. A General
method for confidence intervals. Large sample confidence interval. Test of hypotheses, most
powerful test. Neyman-Pearson lemma. Uniformly most powerful test. Uniformly most powerful
unbiased test. Likelihood ratio test. Sequential tests. Large sample tests.
18
Course Number: STAT 332
Course Name: Designs of Experiments
Credit Hours: 3 (2+2)
Pre-requisite: STAT 102 and STAT 211
Semester Offered: Fall
Course Content : Principles of Experimental Design; Completely Randomized designs; Randomized
Complete Block designs; Latin Square designs; Incomplete Block Designs; Factorial Experiments; Split
Plot; Analysis of Covariance. Statistical software like Minitab, SPSS and R are used.
Course Number: STAT 333
Course Name: Time Series
Credit Hours: 3 (2+2)
Pre-requisite: STAT 231
Semester Offered: Spring
Course Content: This course discusses the analysis of time series data and their use in
prediction and forecasting. The course presents various methods including time series
regression, smoothing techniques and the Box-Jenkins methodology. The emphasize is on the
applied side of the subject utilizing statistical packages like R, SPSS and Minitab.
Course Number: STAT 341
Course Name: Actuarial Statistics I
Credit Hours: 3 (2+2)
Pre-requisite: STAT 102 and STAT 211
Semester Offered: Spring
Course contents: Actuarial models, classifying and creating distributions.Frequency and severity
with coverage models, deductibles, policy limits and coinsuranse. Aggregrate loss models,
compoubd models, computing aggregate claims distributions, comparison beteen the various
computing methods. Discrete and Continuous time ruin models.
19
Course Number: STAT 343
Course Name: Applied Survival Analysis
Credit Hours: 3 (2+2)
Pre-requisite: STAT 102
Semester Offered: Fall
Course contents: Censored data, types of censoring, examples of survival data analysis, the
survival function, the hazard function, Nonparametric Methods, Life tables, the Product-Limit
Estimator of the survival function, comparing two survival distributions (Mantel-Haenszel test),
Parametric Survival Distributions and Inference, Goodness of Fit for Survival, Parametric
Regression Models, Cox’s Proportional Hazards Model. Statistical software like Minitab, SPSS
and R are used.
Course Number: STAT 344
Course Name: Quality Control
Credit Hours: 3 (2+2)
Pre-requisite: STAT 102 and STAT 211
Semester Offered: Spring
Course Content: Analysis of Control Charts for Variables and Attributes; Histogram Analysis; Process
Capability; Standard Acceptance Sampling Plans; Process Reliability. Statistical software like Minitab and
SPSS are used.
Course Number: STAT 361
Course Name: Sampling Methods
Credit Hours: 3 (2+2)
Pre-requisite: STAT 102 and STAT 211
Semester Offered: Spring
Course Content: Principles of sampling; questionnaire Design; Simple random sampling; Stratified and
Cluster Sampling; Ratio and Regression estimation; Systematic Sampling; Multistage and Multiphase
Sampling; Determination of the sample Size; Non-response and Non-sampling Errors Adjustment.
20
Course Number: STAT 371
Course Name: Statistical Packages
Credit Hours: 3 (2+2)
Pre-requisite: STAT 231
Semester Offered: Fall
Course Content: Detailed use and full exploitation of Statistical Packages such as SPSS, MINITAB, R
and SAS in working with Data; Topics include Data Entry, checking, manipulation and Analysis.
Comparison between the different packages, their advantages and disadvantages. Weeknesses and
strengths are discussed. Effective use of Statistical packages in solving real life problems. Advanced
features of statistical packages.
Course Number: STAT 372
Course Name: Statistical Simulation
Credit Hours: 3 (2+2)
Pre-requisite: STAT 211
Semester Offered: Fall
Course Content: Generating of Discrete and Continuous Random Variables; Bootstrapping; Variance
Reduction Techniques; Model Design and Simulation with Applications Including Queuing and other
Applications; Verification and Validation of the Model. Using Statistical software like Minitab, SPSS and R.
Course Number: STAT 381
Course Name: Categorical Data Analysis
Credit Hours: 3 (2+2)
Pre-requisite: STAT 231
Semester Offered: Spring
Course Content : Contingency Tables; Measures of Association; Exact and Asymptotic methods for 2x2
and rxc Contingency Tables; Probit and Logistic Regression Models for Binary Data; Loglinear Models for
Multiway Contingency Tables. Statistical software like Minitab, SPSS and R are used.
21
Course Number: STAT 382
Course Name: Non-Parametric Methods
Credit Hours: 3 (2+2)
Pre-requisite: STAT 221
Semester Offered: Fall
Course Content: Basic Concepts of Non-Parametric Methods; Testing and Estimation for one, Two, and
Several sample Problems; Independent and Paired; Location and Dispersion Problems; Goodness of Fit
Tests; Tests for Trends and Association; Analysis of variance of Ranked Data; Pittman Efficiency of NonParametric Methods. Statistical software like Minitab, SPSS and R are used.
Course Number: STAT 434
Course Name: Generalized Linear Models
Credit Hours: 3 (2+2)
Pre-requisite: STAT 322
Semester Offered: Fall
Course Contents: The Exponential family of distributions, Properties of distributions in the Exponential
family, Generalized linear models, Examples, Inference in Generalized Linear Models, Model Adequacy
and Diagnostics, The deviance statistic, The residuals, modifications of the residuals and model checks
based on the residuals. Special Cases of Generalized Linear Models, Normal theory linear models, Binary
logistic regression, Nominal and ordinal logistic regression, Poisson regression and Loglinear models.
Statistical software like Minitab, SPSS and R are used.
Course Number: STAT 442
Course Name: Actuarial Statistics II
Credit Hours: 3 (2+2)
Pre-requisite: STAT 341
Semester Offered: Fall
Course Content: Construction of Empirical Models, estimation for grouped and modified data,
kernel density estimators. Parametric Statistical methods, estimation and confidence intervals in
actuarial models. Model Selection, graphical methods, goodness of fit techniques. Credibility
theory, Simulation of actuarial models, Case study examples.
22
Course Number: STAT 445
Course Name: Reliability and Life Testing
Credit Hours: 3 (2+2)
Pre-requisite: STAT 322
Semester Offered: Spring
Course Content: Reliability Concepts; Component and System Reliability; Notions of Aging; Lifetime
Distributions and Hazard Functions; Types of Censoring; Nonparametric Estimation of Reliability Function;
Kaplan-Meier and Nelson Estimators; Parametric Inference Procedures for Exponential, Weibull and
Extreme Value Distributions; Proportional Hazards Regression Model; Accelerated Life Testing; StressStrength Models. Statistical software like Minitab, SPSS and R are used.
Course Number: STAT 464
Course Name: Environmental Statistics
Credit Hours: 3 (2+2)
Pre-requisite: STAT 312 & STAT 361
Semester Offered: Spring
Course Content: Stochastic processes in the Environment. Fitting probability models to Environmental
data. Tail Exponential Method. Poisson Processes and its application. Negative binomial model
(Contagion and True Models). Capture-Recapture Method, Distance Sampling, Composite sampling,
Introduction of Rank Set sampling methods, adaptive cluster sampling and adaptive allocation methods.
Course Number: STAT 481
Course Name: Multivariate Analysis
Credit Hours: 3 (2+2)
Pre-requisite: STAT 322 and Math 231
Semester Offered: Fall
Course Content:
Organization of Multivariate Data; Multivariate Distributions; Mahalanobis Distance;
Hotelling's T2; Multivariate Analysis of Variance and Regression; Data Reduction Techniques; Discriminant
23
and Classification Analysis; Canonical Correlation Analysis. Statistical software like Minitab, SPSS and R
are used.
Course Number: STAT 482
Course Name: Bayesian Statistics
Credit Hours: 3 (2+2)
Pre-requisite: STAT 322
Semester Offered: Fall
Course contents: Nature of Bayesian Statistics, Prior and posterior distributions. Noninformative priors.
Jeffereys rule. Conjugate priors. Bayesian Inference, Quadratic loss function and Bayes estimators,
Highest posterior density intervals, Bayesian tests of hypothesis. Bayesian methods in the normal and
some other distributions. Approximate Bayesian Methods, Asymptotic approximations of the Bayes
estimator, The Lindley and Tierney-Kadane methods, Markov chain Monte Carlo methods and the Gibbs
sampler.
Course Number: STAT 498
Course Name: Special Topics
Credit Hours: 3
Pre-requisite: Departmental Approval
Semester Offered: Fall
Course Content: Studies topics in statistics that are not part of the regular offerings. Topics will be
selected by statistics faculty members as appropriate. In each offering, a topic of the choice of the
instructor will be studied in depth as a regular course.
Course Number: STAT 499
Course Name: Graduation Project
Credit Hours: 3
Pre-requisite: Departmental Approval
Semester Offered: Spring
Course Content: A variety of skills learned throughout the curriculum are combined by expecting students
to work through a variety of cases studies. Students are expected to collect data and analyze the data
individually. Oral and written research reports suitable in format and content are required.
24
the Minor in Statistics
25
The Minor in Statistics
Data collection and analysis is an important part in many scientific investigations in various
academic disciplines. Some study programs request the student to take one or two
statistics courses as part of their curriculum. However, in many situations, deeper and more
sophisticated knowledge of Statistics is beneficial, not only during undergraduate studies
and graduation projects, but also in their graduate studies where research, data collection,
data analysis and the related issues are essential. To fullfil this need, the minor in Statistics
is developed where the students are expected to get firm foundation in Statistics so that
they can collect and analyze their data with the help of statistical packages like Minitab,
SPSS and Excel. The following study plan for the Minor in Statistics is designed to help in
achieving these goals and objectives with the desired learning outcomes.
The Study Plan for the Minor in Statistics
College: Arts and Sciences
Dept.: Mathematics, Statistics and Physics
Program: Minor in Statistics
Total hours required: 24 Credit hours
The Minor in Statistics is open for all Qatar University students who major in any field other than
statistics.
Minor Outlines
Compulsive Credit Hours
18
Elective Credit Hours
6
Total
24
Compulsive Courses (18 Cr. Hrs.)
Course No.
Course Name
Pre-requisite(s):
STAT 101
Statistics 1
---
STAT 102
Statistics 2
STAT 101
STAT 211
Introduction to Probability
MATH 102 and STAT 101
26
STAT 231
Applied Regression Analysis
STAT 102 and STAT 211
STAT 361
Sampling Methods
STAT 102 and STAT 211
STAT 371
Statistical Packages
STAT 231
Elective Courses (6 Cr. Hrs)
Credit
hours
Course No.
Course Name
STAT 221
Mathematical
Statistics 1
3
STAT 241
Biostatistics
3
STAT102 or STAT 151
STAT 242
Demography
3
STAT 102
STAT 332
Design of
Experiments
3
STAT 333
Time Series
3
STAT 343
Applied Survival
Analysis
3
STAT 344
Quality Control
3
STAT 102 and STAT 211
STAT 372
Statistical Simulation
3
STAT 211
STAT 381
Categorical Data
Analysis
3
STAT 382
Nonparametric
Statistics
3
Pre-requisite(s)
STAT 211 and MATH 251
STAT 102 and STAT 211
STAT 231
STAT 102
STAT 231
STAT 221
Note: Course descriptions are given in previous section
27
The course MATH 251
“MatheMatics for statistics”
28
The Royal Statistical Society commented that there are necessary mathematical areas not
covered by the courses in the (2004) plan. On the other hand, some mathematical material
that are covered is not needed by statistics students. To solve this problem a new course is
developed which contains the relevant mathematical background needed by statistics
students to replace the earlier courses Calculus 3 and Calculus 4. The course contents are
determined following the recommendations of the Royal Statistical Society and the several
meetings within the statistics program and with the mathematics program. The new course
proposal was submitted for university approval separately by the Mathematics Program.
The course short syllabus is given in the following page.
29
Mathematics for Statistics
123-
Course Number:
Credit Hours:
Prerequisites:
Math 251
3 (4+0)
MATH 102
COURSE OBJECTIVES
450123-
To develop the ability to evaluate limits and differentiate functions of several variables and use them
in some applied problems.
To provide students with the skills of multiple integration for functions of several variables.
To acquaint students with the basic concepts of differential equations with emphasis on first order ordinary
differential equations.
To introduce the students to some basic concepts of numerical analysis.
To make use of Mathematical software as Mathematica in applications.
To introduce Gamma, Beta and Error functions and provide skills to use them for evaluation of some
integrals.
SYLLABUS ITEMS

Functions of Several Variables:
Elementary examples including Quadric surfaces, Limits and Continuity, Notion of differentiability,
Partial derivatives, Mean value theorem, Chain rules, Maximum and Minimum values, Lagrange’s
Multipliers.

Multiple Integrals:
Double integrals and triple integrals, Properties, Evaluation by repeated integrals, Polar
coordinates.

First Order Differential Equations:
Classification, Initial-value problems, Separable variables, Linear equations.

Introduction to partial Differential Equations:
Method of separation of variables for some basic linear partial differential equations.

Numerical Solution of nonlinear equations:
Iterative techniques including the Bisection method for single equations, and the Newton-Raphson
method for nonlinear systems of equations, Applications with Mathematical software.

Numerical Integration:
The Trapezoid rule, The Simpson’s rule, Applications with Mathematical software.
30
Some special functions:
Gamma function, Beta function, Error function, Applications
REFERENCES

Calculus, by James Stewart, 6th Edition, 2008, Brooks/Cole.

Differential Equations With Boundary Problems, D. G. Zill and M. Cullen, 4th Edition, 1997,
Brooks/Cole Publishing Company.

Advanced Engineering Mathematics, Erwin Kreyszig, 7th Edition, 1993, John Wiley and sons, Inc.
Course SYLLABI
31
32
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 101
Statistics I
Course Information
Course Title: Statistics I
Course Number: STAT 101
Credit Hours: 3 (2+2)
Course Status: Major Compulsive Course
Prerequisite: None
Course Description
Basic concepts. Types of data, Sampling methods, Tables and graphs. Descriptive Statistics, Basic
probability concepts,Random experiment. Sample spaces, Rules of probability. Counting techniques.
Conditional probability. Independence, Discrete and continuous random variables. Sampling
distributions, The Student-t distribution, F – distribution and Chi-Square distribution, Point estimation.
Confidence intervals for a single population. Testing hypotheses for a single population. Statistical
software like Excel and Minitab will be used.
Course Objectives
The course aims at:
1234567-
Demonstrating the need for statistical tools, their meaning and concepts.
Acquainying the student with the basic data collection techniques.
Emphasizing the descriptive statistical analysis of data and their interpretation.
Acquainting the student with the basic concepts of probability and probability distributions.
Introducing the concept of sampling distributions and some commonly used ones.
Acquainting the student with the basic concepts and procedures of statistical inference.
Emphasize the use of computers and/or scientific calculators in practical applications.
Learning Outcomes
By the end of this course, students will be able to:
1- Collect some types of data in accordance with statistical principles.
33
2- Describe various types of data numerically and graphically.
Compute basic probabilities.
Use computers to find probabilities and quantiles of some common distributions.
Formulate and solve some basic inferential statistics problems.
Use computers to carry out statistical inference about a population mean, a population proportion
and a population variance.
7- Interpret the results of a data analysis concerning a population mean, a population proportion and a
population variance.
3456-
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Statistics. Population. Types of data. Sampling techniques
Tables and graphs. Displaying quantitative data. Descriptive Statistics
Measure of central tendency, Measures of dispersion
Measures of skewness and kurtosis, Z–scores, Percentiles and Quartiles).
Random experiment. Sample space. Axioms of probability. Rules of probability.
Counting techniques
Conditional probability. Independence. The theorem of total probability. Bayes’
Theorem.
Discrete and continuous random variables. Probability distributions
The Bernoulli, Binomial, and Poisson distributions.
The Normal distribution. The central limit theorem.
Sampling distributions of sample statistics, the mean, median, variance. The
Student-t distribution, F – distribution and Chi-Square distribution.
Point estimation. Confidence intervals for a single population (mean, proportion
and variance)
Testing hypothesis, type 1 error and type 2 error. The power of the test
Testing hypotheses for a single population (mean, proportion and variance
Large sample intervals and tests for the population mean or proportion.
Assessment: Midterm Exams, Final Exam, Assignments, Quizzes.
References
1- Statistics.
McClave and Sincich, 2003, 9th edition, Prentice-Hall.
2- Elementary Statistics.
Bluman, 2008, 7th edition, McGraw-Hill.
3- Introductory Statistics
Neil, A. Weiss, 2008, 8th edition, Addison Wesley.
34
35
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 102
Statistics II
Course Information
Course Title: Statistics II
Course Number: STAT 102
Credit Hours: 3 (2+2)
Course Status: Major Compulsive Course
Prerequisite: STAT 101
Course Description
Chi-Square Procedures. Chi-square goodness of fit test. Contingency tables. Association. Chi-square
test for independence. The completely randomized design. Multiple comparisons. The randomized
block design. The two factor factorial design, Simple regression equation. Inference about the
regression quantities. Nonparametric Statistics, The sign test and Wilcoxon signed rank test, the
Wilcoxon rank sum test. The kruskall-Wallis test. The Friedman test. The Spearman correlation
coefficient. Statistical software like Excel and Minitab will be used.
Course Objectives
The course aims at:
4-
Acquainting students with Chi-Square procedures for testing homogeneity,
independence and goodness of fit.
5-
Introducing the basic ideas of experimental design and analysis of variance.
Giving an introduction to regression and correlation analyses.
Introducing the students to nonparametric techniques and their applications.
67-
Learning Outcomes
By the end of this course, students will be able to:
1- Formulate and test hypotheses concerning frequency data
2- Distinguish between the various type of frequency data collection techniques
3- Analyze data from experimental designs and interpret the results
4- Choose the suitable design for a given problem
5- Conduct regression and correlation analyses and interpret the results
36
6- Check the assumptions of statistical inference procedures and use nonparametric alternatives when
the assumptions are not satisfied
7- Use statistical software to analyze the data
Content Distribution
Topics
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Confidence intervals for the difference of two population means based on paired and
independent samples. Confidence intervals for proportions. Confidence intervals for
the ratio of two variances
Testing hypothesis for the equality of two populations (means, proportions and
variances)
Chi-square goodness of fit test
Contingency tables. Association. Chi-square test for independence
The completely randomized design.
Multiple comparisons
The randomized block design.
The two factor factorial design.
The regression equation. The coefficient of determination
Linear correlation. Inference about the regression quantities.
Prediction. Assumptions and residual plots.
The sign test and Wilcoxon signed rank test for paired samples
The Wilcoxon rank sum test for two independent samples. The kruskall-Wallis test
The Friedman test. The Spearman correlation coefficient
Assessment: Midterm Exams, Final Exam, Assignments, Quizzes.
References
1- Statistics.
McClave and Sincich, 2003, 9th edition, Prentice-Hall.
2- Elementary Statistics.
Bluman, 2008, 7th edition, McGraw-Hill.
3- Introductory Statistics
Neil, A. Weiss, 2008, 8th edition, Addison Wesley.
37
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 211
Introduction to Probability
Course Information
Course Title: Introduction to Probability
Course Number: STAT 211
Credit Hours: 3 (2+2)
Course Status: Major Compulsive Course
Prerequisite: MATH 102 and STAT 101
Course Description
Random experiment. Sample spaces, Events. Axioms and rules of probability. Equally likely sample
spaces. Counting techniques, Conditional probability. Random variables. Expected values. Moment
generating function. Probability generating function, Probability distributions, uniform, Bernoulli,
binomial, geometric, negative binomial, Poisson and hypergeometric. exponential, gamma, beta and
normal. Discrete and continuous bivariate random variables. Joint, Marginal and conditional
distributions.
Course Objectives
The course aims at:
1- Familiarizing the student with the foundations of probability and the basic probability tools and
methods.
2- Acquainting students with random variables and probability distributions.
3- Acquainting students with some discrete and continuous probability models.
4- Introducing some probability theorems and their useful applications.
5- Familiarizing students with some multidimensional random variables.
6- Familiarizing students with some mathematical tools needed in statistics.
Learning Outcomes
By the end of this course, students will be able to:
1- Calculate probabilities and other relevant quantities from probability distributions
2- Select the suitable probability distributions for certain problems
38
3- Derive the expectations, moment generating functions and the cumulative distribution functions
for certain probability distributions
4- Use inequalities and certain theorems to establish certain useful properties of probability
distributions
5- Work with certain multivariate distributions and derive marginal and conditional probability
distributions
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Probability as a long-term behavior of events under identical conditions. Random
experiment. Sample spaces, Events.
Axioms and rules of probability. Equally likely sample spaces.
Counting techniques, Combinations and Permutations,
Combinatoric formulae, Conditional probability. Independence of events
The theorem of total probability. Bayes’ rule
Random variables. Discrete and continuous random variables
Distribution function. Probability mass function and probability density function.
Expected value. Variance. Moments of random variables
Chebychev’s theorem. Moment generating function. Probability generating
function.
Some discrete distributions: uniform, Bernoulli, binomial, geometric, negative
binomial, Poisson and hypergeometric
Some continuous distributions: uniform, exponential, gamma, beta and normal
Moment and probability generating functions for specific distributions
Discrete and continuous bivariate random variables.
Joint, Marginal and conditional distributions
Assessment: Midterm Exams, Final Exam, Assignments, Quizzes.
References
1- John E. Freund's Mathematical Statistics.
Miller & Miller, 7th Edition, 2003, Prentice Hall.
2- Probability and Mathematical Inference.
Hogg and Tanis, 8th Edition, 2009, Prentice Hall.
3- Introduction to Mathematical Statistics.
Hogg, Craig and McKean, 6th Edition, 2004, Prentice Hall.
39
40
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 221
Mathematical Statistics I
Course Information
Course Title: Mathematical Statistics I
Course Number: STAT 221
Credit Hours: 3 (2+2)
Course Status: Major Compulsive Course
Prerequisite: MATH 251 and STAT 211
Course Description
The Multinomial and multivariate normal distributions. Functions of random variables. Transformation
2
techniques. Sampling Distributions, the t, the  , and the F distributions. The distribution of a single
order statistic. The joint distribution of two order statistics. Distributions of functions of order statistics.
Limit Theorems, Convergence in distribution, Convergence in Probability, Laws of large numbers.
Limiting distributions. The Central limit theorem
Course Objectives
The course aims at:
1- Acquainting students with some basic statistical tools needed to develop some
statistical theorems and applications.
2- Developing the skills needed to obtain sampling distributions of some important
statistics.
3- Acquainting the students with the basic theory of order statistics and the related problems.
4- Developing the important ideas of limiting distributions and convergence of random variables
and their use in statistics.
Learning Outcomes
By the end of this course, students will be able to:
1- Obtain the distribution of certain functions of random variables
41
2- Obtain the distributions of order statistics and the related quantities
3456-
Prove some basic mathematical statistics theorems
Use theorems to derive the sampling distributions of some statistics
Derive the large sample distributions of some important statistics
State, prove and use the central limit theorem and laws of large numbers
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Special multivariate distributions, the Multinomial
The multivariate normal distributions.
Functions of a single random variable. Transformation techniques. Jacobians. Distribution
function technique
Functions of more than one random variable. Transformation techniques. Jacobians.
Distribution function technique
The moment and probability generating function technique
2
Sampling from the normal distribution. Distribution of mean and variance. The t, the  , and
the F distributions.
The distributions of a single and two order statistics.
Distributions of functions of order statistics like the range.
Convergence in distribution
Convergence in Probability
Laws of large numbers
Limiting distributions
The Central limit theorem
Applications
Assessment: Midterm Exams, Final Exam, Assignments, Quizzes.
References
1-
John E. Freund's Mathematical Statistics.
Miller & Miller, 7th Edition, 2003, Prentice Hall.
2-
Introduction to Mathematical Statistics.
Hogg, Craig and McKean, 6th Edition, 2004, Prentice Hall.
3-
An Introduction to mathematical Statistics.
By Larsen and Mood, 4th Edition, 2005, Prentice Hall.
42
43
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 231
Applied Regression Analysis
Course Information
Course Title: Applied Regression Analysis
Course Number: STAT 231
Credit Hours: 3(2+2)
Course Status: Major Compulsory Course
Prerequisite: STAT 102 and STAT 211
Course Description
This course covers regression models with emphasis on linear regression models. Model fitting and
checking procedures. Model building and model adequacy checking. Diagnostics with remedial
procedures. Inference techniques on the regression quantities are considered with applications to many
real life problems. Statistical software like Minitab, SPSS and R will be used.
Course Objectives
The course aims at:
1- Introducing simple regression and correlation analysis with the model building
process.
2- Acquainting students with methods and concept of multiple regression and
correlation.
3- Developing the ability to build regression models.
4- Acquainting students with the non linear regression theory.
5- Familiarizing the student with the statistical software tools used for applying regression
analysis
Learning Outcomes
By the end of this course, students will be able to:
1- Fit simple linear regression models
2- Interpret the results of the simple linear regression analysis
44
3- Build Multiple regression models
4- Check regression assumptions and undertake remedial actions
5- Use statistical software like Minitab, R or SPSS
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Revision of some key concepts in statistics and preparation to the coming course
contents
Simple linear Regression models.
Least squares estimation of regression parameters.
Inference in simple regression models
Diagnostics and remedies
Applications
Multiple regression models. General Linear regression model in matrix terms.
Estimation of regression coefficients.
Fitted values and residuals. Analysis of variance results. Inferences about regression
parameters. Estimation of mean response and prediction of new observation.
Diagnostics and remedial measures. Applications
Use of indicators variables as regressors.
Overview of model-building process. All-Possible-Regression procedures for
variables reductions. Forward stepwise Regression and other automatic-search
procedures for variables reductions
Applications
Identifying outlying Y observations: studentized deleted residuals. Identifying
outlying X observations: hat matrix.
Multicolinearity. Influential observations, Remedial measures
Nonlinear regression models
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1- Applied Linear Regression Models.
Neter Kutner Nachtshem Wasserman, 4th Edition, 2004, Irwin.
2- Regression Analysis by Examples.
Samprit Chatterjee and Hadi, A., 4th Edition, 2006, John Wiley and sons, Inc.
3- Applied Regression Analysis.
Draper and Smith, Press, 3rd Edition, 1998, John Wiley and sons, Inc.
45
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 241
Biostatistics
Course Information
Course Title: Biostatistics
Course Number: STAT 241
Credit Hours: 3(2+2)
Course Status: Major Elective Course
Prerequisite: STAT 102
Course Description
Methods of Sampling in Medical Studies; Summarizing and Presenting Medical Data; Demographic
Statistics; Survival Analysis; Analysis of Cross Tabulation; Inference for Means; Parametric and NonParametric with applications to medical data; Multiple Linear, Logistic, Poisson and Cox regression applied
to medical data; Sample Size Determination. Statistical software like Minitab and Excel are used.
Course Objectives
The course aims are:
1- To familiarize students with basic methods of sampling for collection of data and
use of follow-up surveys in biomedical and health studies..
2- To review different methods of estimation of parameters, testing of hypothesis and
regression models with applications to medical studies.
3- To introduce analysis of contingency tables techniques relevant to medical data.
4- To introduce the design of biostatistical studies
5- To familiarize students with different measures of Demography and life tables.
Learning Outcomes
By the end of this course, students will be able to:
1- Present and describe medical data
2- Construct and interpret life tables
3- Calculate and interpret some biostatistical measures like the odds ratio.
46
4- Analyze survival regression models like the proportional hazards and the parametric life
regression models.
5- Analyze data in the form of contingency tables arising from biostatistical designs
6- Use statistical software like Minitab, R or SPSS for data analysis
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Basic techniques of data collection
Cross-sectional data, Follow-up surveys
Elements of estimation and testing of hypothesis with applications to medical data
Simple linear regression applied problems arising in medical studies
Analysis of variance for medical data designs
Contingency tables. Relative risk. Odds ratio
Test of independence. Test for goodness of fit, Applications
Nonparametric methods with medical data
Measures of mortality
Life-Tables and follow up studies
Measures of fertility. Measures of population growth.
Concept of stable populations. Projection of population.
Logistic regression
Survival regression models, Cox’s regression model
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1-
Introductory Biostatistics.
Chap T. Lee, 2003, 1st edition, John Wiley, N. Y.
2-
Biostatistics: A Foundation for Analysis in Health Sciences.
Wayne. W. Daniel, 1998, 7th edition, John Wiley and Sons, Inc.
3-
Applied Statistics.
Parimal Mukhopadhay, 1999, New Central, Calcutta.
4-
Medical Biostatistics.
Abhaya Indrayan, Series Volume: 7, 2000, Marcel Dekker, Inc.
5-
An Introduction to Medical Statistics.
Martin Bland, 3rd edition, 2000, Oxford Press.
47
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 242
Demography
Course Information
Course Title: Demography
Course Number: STAT 242
Credit Hours: 3 (2+2)
Course Status: Major Elective Course
Prerequisite: STAT 102
Course Description
Basic Concepts, Meaning of population, Demographic rates. Period rates. Person years. Growth rate.
The concept of cohort. The crude death rate. Age-specific death rates. The Lexis diagram. Mortality
rates. Single-failure indices. The standardized death rate. The standardized mortality ratio. Life Tables,
Multiple Decrement Life Tables, Fertility and Reproduction, Modeling Age Patterns
Course Objectives
The course aims are:
1- To acquaint the student with the basic concepts in demography including the
population and the rates of various types.
2- To acquaint the students with the methods of calculating Age-Specific rates and
probabilities.
3- To give the student an introduction to life tables and multiple decrement life tables.
4- To introduce the students to fertility rates, cohort fertility and reproduction measures.
5- To give the student a good knowledge in population projections and modeling age patterns
Learning Outcomes
By the end of this course, students will be able to:
12345-
Calculate the crude death rate, age specific death rates and mortality rates
Construct and use life tables
Use multiple decrement life tables
Analyze fertility data
Analyze age patterns of migration
48
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topic
Meaning of population. Demographic rates. Period rates.
Person years. Growth rate. The concept of cohort
The crude death rate. Age-specific death rates
The Lexis diagram. Mortality rates
Single-failure indices. The standardized death rate. The standardized mortality ratio.
The life table. Life table construction
Life table interpretation. Life tables and mortality
Multiple decrement life tables and its algebra
Dependent and independent death rates
Fertility rates. Age specific fertility rates
Period fertility. Cohort fertility.
Age patterns of mortality. Age patterns of fertility
Age patterns of migration
Birth interval analysis
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects.
References
1- Demographic Methods
Hinde, A. (1998). Arnold, London
2- Demographic methods and concepts
Rowland, D.T. (2003). Oxford Press
49
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 312
Stochastic Processes
Course Information
Course Title: Stochastic Processes
Course Number: STAT 312
Credit Hours: 3(2+2)
Course Status: Major Compulsory Course
Prerequisite: STAT 211 and MATH 251
Course Description
Elements of Stochastic Processes; Discrete Time Markov Chains; Random Walks; Branching
Processes; Poisson Processes; Birth and Death Processes; Queuing Systems; Renewal Processes.
Basic theory of martingales and Brownian motion. Aapplications to stochastic financial modeling.
Course Objectives
The course aims are:
1- To develop an awareness of the use of stochastic processes to build adequate mathematical
models for random phenomena evolving in time.
2- To understand notions of long-time behavior including transience, recurrence, and equilibrium to
answer basic questions in several applied situations including branching processes and random
walk.
3- To introduce students to basic concepts, techniques and results associated primarily with the
elementary theory of Markov processes.
4- To introduce students to basic queuing models involving exponential arrivals and departures.
5- To familiarize the student with concepts of Matingales and Brownian motion.
6- To familiarize the student with some applications of stochastic processes in finanancial modeling.
Learning Outcomes
By the end of this course, students will be able to:
1- Construct transition matrices in Markov chains and calculate various types of transition
probabilities
50
23456-
Classify states and Markov chains according to their long term behavior
Use Poisson processes for modeling various phenomena
Use queuing models with exponential arrivals and departures to model real life situations
Derive the probabilities for the birth death process and renewal theory
Calculate measures of performance of systems modeled by stochastic processes
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Definitions, basic concepts and classification of general stochastic
processes.
Markov property, Chapman-Kolmogorov equations
Representation of chains using digraphs and stochastic matrices
Classification of states, Ergodicity
Limiting behavior of Markov chains
Random walks (absorption probability, mean time to absorption)
Branching processes (Galton-Watson criticality theorem, extinction
probabilities)
Definition, Poisson process
Pure birth and pure death processes, birth and death processes
Measures of effectiveness, M/M/1
M/M/s and M/G/1 queues
Applications in Reliability
Martingales and Brownian motion
Applications in financial modeling
Assessment: Midterm Exams, Final Exam, Assignments, Quizzes.
References
1-
An Introduction to Stochastic Modeling.
H. M. Taylor and S. Karlin, 3rd Edition, 2003, Academic Press.
2-
Introduction to Stochastic Processes
Gregory F. Lawler, 2nd edition, 2006, CRC Press.
3-
Introduction to Probability Models.
S. M. Ross, 9th Edition, 2006, Academic Press.
4-
Essential of Stochastic Processes.
R. Durrett, 2nd Edition, 1999, Springer Verlag.
51
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 322
Mathematical Statistics II
Course Information
Course Title: Mathematical Statistics II
Course Number: STAT 322
Credit Hours: 3 (2+2)
Course Status: Major Compulsive Course
Prerequisite: STAT 221
Course Description
Consistency, Sufficiency, the exponential family of distributions. Completeness of a family of
distributions. Theory of Point Estimation, Criteria for judging point estimators. The mean
squared error and the variance. Unbiasedness, Rao-Blackwell Theorem. Uniformly minimum
variance unbiased estimation. Lower bounds of the variance of unbiased estimators.
Information. Efficiency of an estimator. Maximum likelihood method. Moments method. Least
squares method. Comparisons between the different methods. Interval estimation, Pivotal
quantities. A General method for confidence intervals. Large sample confidence interval. Test
of hypotheses, most powerful test. Neyman-Pearson lemma. Uniformly most powerful test.
Uniformly most powerful unbiased test. Likelihood ratio test. Sequential tests. Large sample
tests.
Course Objectives
The course aims are:
1- To acquaint students with some basic statistical concepts needed to develop
some statistical estimation and testing theorems and applications.
2- To familiarize students with methods of statistical inference under various probability
models and how to apply them.
3- To develop the optimality criteria used for estimation and testing.
4- To introduce sequential and large sample tests
Learning Outcomes
By the end of this course, students will be able to:
52
1- Classify distributions belonging to the exponential family of distributions
2- Use effectively the properties of the exponential family of distributions to derive
statistical inference procedures
3- Use the optimality criteria to compare the competing inference procedures
4- Derive point estimators like the maximum likelihood, the least squares, the moments and
the minimum variance unbiased estimators
5- Derive most powerful and likelihood ratio tests
6- Construct confidence intervals and study their properties
7- Derive large sample test
8- Apply sequential tests
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Consistency of an estimator. Sufficiency of a statistic
Exponential family of distributions. Completeness of a family of distributions
Criteria for judging point estimators. The mean squared error and the variance.
Unbiasedness
Rao-Blackwell Theorem. Uniformly minimum variance unbiased estimation
Lower bounds of the variance of unbiased estimators. Information. Efficiency of an
estimator
Maximum likelihood method
Moments and Least squares method, Comparisons
Pivotal quantities
A General method for confidence intervals
Large sample confidence interval
Basic concepts. Most powerful test. Neyman-Pearson lemma
Uniformly most powerful test. Uniformly most powerful unbiased test
Likelihood ratio test
Sequential tests. Large sample tests
Assessment: Midterm Exams, Final Exam, Assignments, Quizzes.
References
1- John E. Freund's Mathematical Statistics.
Miller & Miller, 7th Edition, 2003, Prentice Hall.
2- Probability and Mathematical Inference.
Hogg and Tanis, 8th Edition, 2009, Prentice Hall.
3- Introduction to Mathematical Statistics.
Hogg, Craig and McKean, 6th Edition, 2004, Prentice Hall.
53
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 341
Actuarial Statistics I
Course Information
Course Title: Actuarial Statistics I
Course Number: STAT 442
Credit Hours: 3 (2+2)
Course Status: Program Elective Course
Prerequisite: STAT 102 and STAT 211
Course Description
Actuarial models, classifying and creating distributions.Frequency and severity with coverage models,
deductibles, policy limits and coinsuranse. Aggregrate loss models, compoubd models, computing
aggregate claims distributions, comparison beteen the various computing methods. Discrete and
Continuous time ruin models.
Course Objectives
The course aims at:
1- Acquainting the student with actuarial models and the related quantities
2- Familiarize the student with methods of calculating deductibles and studying their effect on
claim frequency and the effect of inflation on them
3- Gain knowledge on aggregate loss distributions and the related calculations
4- Acquainting the student with stochastic processes associated with insurance including discrete
and continuous ruin probabilities
Learning Outcomes
By the end of this course, students will be able to:
1- Derive and work with actuarial probability models and the related functions
54
2- Calculate deductibles and study their effects on claim frequency and how they are affected by
inflation
3- Compute aggregate claim distributions with recursive methods and approximate methods
4- Develop and use stochastic models for insurance
5- Derive continuous and discrete ruin probabilities
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Introduction to Actuarial Science, Examples
Actuarial probability models
Functions associated with probability distributions
Creating new distributions, Mixture distribution
Deductibles, the loss elimination ratio, the effect of inflation for ordinary deductibles
Coinsurance, the impact of deductibles on claim frequency
Aggregate loss models, model choices
The compound model for aggregate claims, computing the aggregatre claims distribution
Recursive methods
calculations with approximate distributions
Exact calculaions of the aggregate distribution, Compound Poisson approximation
Process models for insurance, Discrete ruin probabilities
Continuous time ruin models
Examples and Applications
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects.
References
1- Loss Models: From Data to Dicisions
Stuart A. Klugman, Harry, H. Panjer and Gordon E. Willmot, 3rd edition, Wiley InterScience.
2- Modern Actuarial Risk Theory
Rob Kaas, Marc Goovaerts, Jan Dhaene and Michel Denoit, 2nd edition, Springer.
3- Modern Actuarial Theory and Practice
Philip Booth, Robert Chadburn, Steve Haberman and Dewi James, 2nd edition, Chapman and
Hall/CRC
55
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 332
Design of Experiments
Course Information
Course Title: Design of Experiments
Course Number: STAT 332
Credit Hours: 3(2+2)
Course Status: Major Compulsory Course
Prerequisite: STAT 231
Course Description
Principles of Experimental Design; Completely Randomized designs; Randomized Complete Block
designs; Latin Square designs; Incomplete Block Designs; Factorial Experiments; Split Plot; Analysis of
Covariance. Statistical software like Minitab and R will be used.
Course Objectives
The course aims at:
1234-
Acquainting students with single factor experiments.
Familiarizing the student with multiple comparisons procedures
Introducing some special designs that have a wide variety of applications.
Acquainting students with factorial experiments and higher designs that have a wide variety
of applications.
5- Acquainting the student with the distribution theory of statistics used in analysis of variance
techniques.
Learning Outcomes
By the end of this course, students will be able to:
1- Design statistical experiments which conforms to the basic statistical principles of experimental
design
2- Write down the statistical model for the single factor, block, factorial and related designs and
estimate their parameters
3- Construct the relevant ANOVA table for the given design and interpret the results
4- Perform various types of multiple comparisons procedures when needed
56
5-
Use statistical software to obtain the results of the analysis of a designed experiment and interpret
their values.
6- Derive and prove some basic distributional properties related to F tests.
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Experiments with Single factor studies
The Completely randomized design
Multiple Comparisons
Randomized block
Latin squares, related designs
Applications
Factorial designs
2 k factorial designs
3 k factorial designs
Applications
Random factors and Mixed models
Rules for the expected mean squared error
Nested and Split Plot designs
Analysis of Covariance
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1-
Design and Analysis of Experiments.
D. C. Montgomery, 7th Edition, 2007, John Wiley and sons, Inc.
2-
Statistical Design and Analysis of Experiments.
Mason, Gunst and Hess, 2nd Edition, 2003, John Wiley and sons, Inc.
3-
Fundamental Concepts in the Design of Experiments.
Charles Hicks, 5th Edition, 1999, Oxford University Press.
57
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 333
Time Series
Course Information
Course Title: Time Series
Course Number: STAT 333
Credit Hours: 3 (2+2)
Course Status: Major Compulsory Course
Prerequisite: STAT 231
Course Description
This course discusses the analysis of time series data and their use in prediction and forecasting. The
course presents various methods including time series regression, smoothing techniques and the BoxJenkins methodology. The emphasize is on the applied side of the subject utilizing statistical packages
like R, SPSS and Minitab.
Course Objectives
The course aims at:
Introducing the concept of a time series and the nature of time series data.
12345-
Giving a firm knowledge on how and when to apply the time series methodology.
Introducing smoothing techniques and their use in time series data
Developing the Box-Jenkinz methodology for time series data
Giving practice in analyzing real world problems and interpret the results.
Building a solid theoretical background for the subject.
Learning Outcomes
By the end of this course, students will be able to:
1234567-
Analyze various types of time series regression models.
Use decomposition and smoothing techniques
Apply the Box-Jenkins methodology for time series data.
Use packages to implement decomposition and Box-Jenkinz methods
Conduct real life studies involving time series
Produce and interpret the computer output of various packages for the time series analysis.
Explain the theoretical basis of the methods of time series analysis
58
Content Distribution
Week
1
2
3
4
5
6
8
9
10
11
12
13
14
Topics
Introduction and general ideas
The nature of time series data and forecasting
Time series regression
Model checks, autocorrelation, transformation, dummy variables
Decomposition methods
Applications
Single Exponential smoothing
Double exponential smoothing
Holt-Winter’s methods
Nonseasonal Box-Jenkinz methods
Diagnostics and forecasting
Box-Jenkinz seasonal modeling
Applications
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1- Forecasting, Time series and Regression: an applied approach.
B. Bowerman, R. O'Connell and Anne. Koehler, 4th edition, 2004, South Western College
Publications.
2- Time Series Models.
Harvey, A.C., 2nd Edition, 1993, Harvester Wheatsheaf.
3- Time Series Analysis, Forecasting and Control.
G. Box, G Jenkins and G. Reinsel, 4th Edition, 2008, Wiley.
59
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 343
Applied Survival Analysis
Course Information
Course Title: Applied Survival Analysis
Course Number: STAT 343
Credit Hours: 3 (2+2)
Course Status: Major Elective Course
Prerequisite: STAT 102
Course Description
Censored data, types of censoring, examples of survival data analysis, the survival function, the
hazard function, Nonparametric Methods, Life tables, the Product-Limit Estimator of the survival
function, comparing two survival distributions (Mantel-Haenszel test), Parametric Survival Distributions
and Inference, Goodness of Fit for Survival, Parametric Regression Models, Cox’s Proportional
Hazards Model. Statistical software like Minitab, SPSS and R are used
Course Objectives
The course aims at:
1-
Introducing censored data and presenting the special features associated with them
2-
Acquainting the student with the statistical models used in survival analysis and their
properties.
3-
Introducing the concept of covariate and how to study their effects on survival times
4-
Developing the skills, including using statistical software, needed to handle practical
situations with survival analysis.
5-
Stimulating interest to go for advanced studies in survival analysis.
Learning Outcomes
By the end of this course, students will be able to:
1- Derive the survival function, the hazard function and other related quantities in survival
analysis
60
234567-
Identify suitable distributions for the given data using probability and hazard plotting
Compute nonparametric estimators like the product-limit estimator
Construct life tables
Compare survival experience of two or more groups of individuals
Study the effect of covariates on survival time using regression models
Use statistical software for the analysis of survival data
Content Distribution
Week
1
2
3
4
5
6
8
9
10
11
12
13
14
Topics
Censored data, types of censoring, examples of survival data analysis
the survival function, the hazard function
Life tables, the Product-Limit Estimator of the survival function
Comparing two survival distributions (Mantel-Haenszel test)
The Exponential and Weibull distributions
The Lognormal, Gamma and Log-logistic distributions
Other survival distributions
Inference in survival models with covariates
Probability plotting, hazard plotting
Cox- Snell residuals, goodness of fit based on likelihood asymptotics
Exponential regression, Weibull regression
Lognormal regression, Model selection
Estimation and testing in the proportional hazards model
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1- Analysis of Survival Data
D.R. Cox and D. Oakes, Chapman & Hall, 1984. L. Prentice, Wiley, 2002.
2- Statistical Models and Methods for Lifetime Data, 2nd Ed.
J.F. Lawless, Wiley,2003.
3- Modeling Survival Data, Extending the Cox Model
T.M. Therneau and P.M. Grambsch, Springer, 2000.
61
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 344
Quality Control
Course Information
Course Title: Quality Control
Course Number: STAT 344
Credit Hours: 3(2+2)
Course Status: Major Elective Course
Prerequisite: STAT 102 and STAT 211
Course Description
Analysis of Control Charts for Variables and Attributes; Histogram Analysis; Process Capability;
Standard Acceptance Sampling Plans; Process Reliability. Statistical software like Minitab, SPSS and
R are used
Course Objectives
The course aims are:
1- To acquaint students with control charts of variables and attributes.
2- To introduce process capability and its assessments.
3- To learn various sampling plans and their properties.
Learning Outcomes
By the end of this course the student will be able to:
12345-
Construct, use and interpret control charts for the mean
Construct, use and interpret control charts for attributes
Calculate measures of process capability and interpret the results
Design and analyze acceptance sampling plans
Use statistical software to construct control charts and analyze acceptance sampling plans
62
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Statistical basics for control charts. Rational sub grouping
Analysis of patterns of control charts. Uses of control charts
Construction and use of sample mean and sample range charts. Sample mean and sample
standard deviation charts
The operating characteristic function. The average run length for the charts. Individuals
charts.
Binomial count charts. Construction and use of the p chart for constant and variable
subgroup sizes
The np charts. Area of opportunity charts. c and u charts
Applications and examples
Process capability ratios (PCR). Confidence intervals on PCR
The relationships between control limits. Natural limits and specification limits.
Acceptance sampling by attributes. The operating characteristic curves
The single-, double-, and sequential-sampling plans
Rectifying inspection. The Average outing quality
Acceptance Sampling by Variables.
Applications and examples
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1-
Introduction to Statistical Quality Control.
Montgomery, D.C., 6th Edition, 2008, John Wiley and sons, Inc.
2-
Quality Control.
D. H. Besterfield, 8th edition, 2008, Prentice Hall.
3-
Statistical Quality Control.
Chandra, M. J, 2001, CRC Press.
63
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 361
Sampling Methods
Course Information
Course Title: Sampling Methods
Course Number: STAT 361
Credit Hours: 3(2+2)
Course Status: Major Compulsory Course
Prerequisite: STAT 102 and STAT 211
Course Description
Principles of sampling; questionnaire Design; Simple random sampling; Stratified and Cluster
Sampling; Ratio and Regression estimation; Systematic Sampling; Multistage and Multiphase
Sampling; Determination of the sample Size; Non-response and Non-sampling Errors Adjustment.
Course Objectives
The course aims are:
1- To familiarize students with the concepts of a finite population, sample, sampling design,
estimator and advantages of a sample survey over complete enumeration.
2- To acquaint students with the concepts of simple random sampling, with and without
replacement for estimation of population mean, total and proportion.
3- To introduce students to the concepts of stratified, systematic and cluster random sampling for
estimation of population total, proportion and mean.
4- To introduce the concept of ratio estimation and regression estimation for estimation of a population
total and population mean.
5- To introduce the concept of probability proportional to size with replacement (PPSWR) sampling.
6- To introduce the concepts of multistage sampling, multiphase sampling, non-sampling error and
methods for non-response.
64
Learning Outcomes
By the end of the course the student will be able to:
1- Design and conduct sample surveys
2- Calculate and interpret estimators obtained from simple random samples, stratified, systematic,
cluster and other related samples
3- Calculate and interpret ratio and regression estimators
4- Use the pps sampling design and interpret the results
5- Distinguish nonsampling errors and make necessary adjustments
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Finite population. Population parameters. Sample. Sampling design.
Estimators. Advantages of sampling. Conducting large scale sample surveys.
Sampling with and without replacement
Estimation of population total, mean and proportion with their variance
estimators
Estimation of domain total. Stratified sample
Systematic sample and cluster sample
Ratio and regression estimators of the population total.
MSE of ratio estimators. Bias of estimators. Efficiency.
Selection of sample. Estimation of population total and variance.
Simple random sampling at both stages. PPSWR-sampling at first stage.
Stratified multi-stage sampling.
Adjustment for non-response in surveys.
Sampling with probability proportional to size
Estimation of parameters with PPS sampling
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects.
References
1-
Sampling Methodologies and Applications.
P. Rao, 2000, Chapman and Hall/CRC, Inc.
2-
Theory and Methods of Survey Sampling.
Parimal Mukhopadhay, 1998, Prentice-Hall of India.
3-
Elementary Survey Sampling.
R. Scheaffer, W. Mendenhall III and R. Ott, 6th Edition, 2005, Duxbury Press.
65
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS & PHYSICS
STAT 371
Statistical Packages
Course Information
Course Title: Statistical Packages
Course Number: STAT 371
Credit Hours: 3 (2+2)
Course Status: Major Compulsory Course
Prerequisites: STAT 231
Course Description
Detailed use and full exploitation of Statistical Packages such as SPSS, MINITAB, R and SAS in working
with Data; Topics include Data Entry, checking, manipulation and Analysis. Comparison between the
different packages, their advantages and disadvantages. Weeknesses and strengths are discussed.
Effective use of Statistical packages in solving real life problems. Advanced features of statistical
packages like programming.
Course Objectives
The course aims are:
1- To study, in detail, the standard statistical packages to students and how to effectively use them.
2- To get knowledge on how to obtain and manipulate the various types of plots and descriptive
measures.
3- To familiarize the students with the computations of statistical tables, critical values and other
related quantities.
4- To get practice in solving real world problems and interpretation of the results.
5- To get knowledge on how to apply the advanced statistical techniques and how to build models that
can be used for statistical inference.
6- To compare between different statistical packages, their advantages, strengths and special features
Learning Outcomes
By the end of this course, students will be able to:
1- Use effectively some of the most important statistical packages.
2- Manipulate data effectively with various computer packages
66
34567-
Produce and manipulate descriptive measures, graphs and other related quantities
Obtain certain characteristics of probability distributions
Analyze various types of real life data using statistical packages
Interpret the output of the data analysis and write reports
Perform simulation techniques on some standard distributions
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Introduction to Packages, getting started
Manipulating data and variables in R, SPSS and SAS
Manipulating data and variables in R, SPSS and SAS
Producing summary Statistics and graphs
Working with Statistical Distributions, plotting their densities and distribution
functions
Working with Statistical Distributions, calculating probabilities, finding quantiles
and critical values
Applications
Linear Regression and Correlation
T – test procedures, one sample, paired samples and independent samples
ANOVA techniques and Chi-Square tests
Applications
Simulation from discrete and continuous distributions
Programming in statistical packages, R
Programming in statistical packages, SAS
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1- SPSS Survival manual
J. Pallant, 2nd edition, 2005, Open University Press.
2- Doing data analysis with MINITAB 14
M. Carver, 2nd edition, 2003,Duxbury Press.
3- Using SPSS for Windows
Green, Salkind and Akey, 5TH edition, 2007, Prentice Hall.
67
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 372
Statistical Simulation
Course Information
Course Title: Statistical Simulation
Course Number: STAT 372
Credit Hours: 3(2+2)
Course Status: Major Elective Course
Prerequisite: STAT 211
Course Description
This course covers the basic ideas of statistical simulation including: Generating of Discrete and
Continuous Random Variables; Bootstrapping; Variance Reduction Techniques; Model Design and
Simulation with Applications Including Queuing and other Applications; Verification and Validation of the
Model. Using Statistical software like Minitab, SPSS and R.
Course Objectives
The course aims are:
1- To acquaint students with methods of generating uniform random numbers.
2- To equip the student with general and special techniques for generating variates from discrete and
continuous distributions.
3- To give an introduction to the principles of variance reduction.
4- To introduce the students to some applications of simulation including the simulation of Poisson
processes and queuing systems.
5- To acquaint the students with the techniques of Jackknife and Bootstrap for calculating variance
estimates and confidence intervals.
Learning Outcomes
By the end of this course, students will be able to:
1- Generate uniform random numbers manually as well as using the computer.
2- Write and run a variety of computer programs using R-project packages.
3- Recognize and apply different techniques for generating random numbers from discrete and
continuous distributions.
4- Identify and use principles of variance reduction techniques.
68
5- Analyze and apply statistical simulation methods in interdisciplinary issues within political, social,
economic and statistical modeling.
6- Use different simulation techniques for statistical computations including Jackknife and Bootstrap.
7- Use statistical software for simulation studies.
Content Distribution
Week
1
2
4
5
6
7
8
9
10
11
12
13
14
Topics
Introduction & Motivation
Introduction to R
Uniform Random Numbers: Linear and multiplicative linear congruential generators.
Tests for random numbers. Empirical tests. Shuffling
General Methods for Generating Random Variates
Inversion of cumulative distribution function
Generation of Variates From Some Standard Distributions: Standard normal distribution and the
Box-Muller method.
Lognormal, Beta, t, Gamma, binomial, negative binomial and Poisson distributions
Variance Reduction methods 1: Importance sampling Stratified sampling
Variance Reduction methods 2: Control variates index numbers
Rejection methods. Adaptive rejection methods
Discrete Event Simulation: Poisson processes, Time-Dependent Poisson distributions, Markov
chains. Queuing systems.
The Jackknife and the Bootstrap.
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1. Simulation and the Monte Carlo Method
R. Rubinstein and D. Kroese, Second edition, 2008, Wiley
2.
Simulation and Monte Carlo
J.S. Dagpunar, 2007, Wiley.
3.
A Course in Simulation
Sheldon Ross, 2002, 3rdedition, Academic Press.
69
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 381
Categorical Data Analysis
Course Information
Course Title: Categorical Data Analysis
Course Number: STAT 381
Credit Hours: 3(2+2)
Course Status: Major Elective Course
Prerequisite: STAT 231
Course Description
Contingency Tables; Measures of Association; Exact and Asymptotic methods for 2x2 and rxc
Contingency Tables; Probit and Logistic Regression Models for Binary Data; Loglinear Models for
Multiway Contingency Tables. Statistical software like Minitab, SPSS and R are used.
Course Objectives
The course aims are:
1- To introduce the most important methods for analyzing categorical data.
2- To familiarize the student with high dimensional contingency tables and the relevant statistical
models.
3- To acquaint students with the methods of analyzing logistic and Poisson models.
4- To familiarize the students with the methods of checking the fit of models and how to build
suitable models for a given categorical data.
Learning Outcomes
By the end of this course, students will be able to:
12345-
Test hypotheses associated with contingency tables and interpret the results.
Calculate certain descriptive measures from contingency tables.
Apply logistic regression and log linear models for categorical data and interpret the results
Check model adequacy and build relevant models.
Use effectively statistical software to analyze and interpret the results.
70
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Basic concepts. Categorical data. Cross-classification tables.
Structure of contingency tables
Comparing proportions in two way tables. Odds ratio
Relative risk, Tests of independence,
Exact tests
Partial associations. Cochran-Mantel Haneszel methods.
Exact inferences for conditional associations
Interpreting logistic regression model. Inference for logistic regression.
Model checking
Logit models, multiple logistic regression and exact inference
Log linear models for two way tables. Inferences for Log linear models.
Modeling ordinal associations. Testing conditional independence
Model fitting and checking
Applications and examples
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1-
An Introduction to Categorical Data Analysis.
Alan Agresti, 1st Edition, 1996, John Wiley and sons, Inc.
2-
Applied linear regression models.
Wasserman, Netter and Kutner, 3rd Edition, 1996, McGraw-Hill.
3-
Analysis of Ordinal Categorical Data.
Alan Agresti, 1984, John Wiley and sons, Inc.
71
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 382
Nonparametric Statistics
Course Information
Course Title: Nonparametric Statistics
Course Number: STAT 382
Credit Hours: 3(2+2)
Course Status: Major Elective Course
Prerequisite: STAT 221
Course Description
Basic Concepts of Non-Parametric Methods; Testing and Estimation for one, Two, and Several sample
Problems; Independent and Paired; Location and Dispersion Problems; Goodness of Fit Tests; Tests
for Trends and Association; Analysis of variance of Ranked Data; Pittman Efficiency of Non-Parametric
Methods. Statistical software like Minitab, SPSS and R are used.
Course Objectives
The course aims are:
123456-
To introduce the basic concepts of nonparametric methods.
To present students with problems of estimation.
To familiarize students with testing of hypotheses for a single sample problem.
To acquaint students with testing of hypotheses for a two-sample problem.
To acquaint students with testing of hypothesis for c-sample problems.
To familiarize students with different tests and measures of association from contingency tables.
Learning Outcomes
By the end of this course, students will be able to:
123456-
Conduct nonparametric tests for single sample problems
Conduct nonparametric tests for the two sample problems
Conduct nonparametric tests for the multi- sample problems
Calculate and interpret several measures of correlation and contingency
Calculate nonparametric estimators and confidence intervals for population parameters
Use statistical software for nonparametric data analysis
72
Content Distribution
Weeks
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Scope of nonparametric methods with respect to parametric methods.
Single-sample problem: test of randomness. Test of goodness of fit
Tests of location. Sign test. Wilcoxon signed-rank test
Hodges-Lehmann estimators, confidence intervals
Wald-Wolfwitz Run test. Mann-Whitney-Wilcoxon test
Median test. Kolmogorov-Smirnov two-sample test
Tests of independence, runs tests
Tests for Dispersion
Kruskal-Wallis test. Friedman’s test
Other multi-sample tests
Test of independence. Test for homogeneity
Yule’s coefficient of correlation. Pearson’s coefficient of contingency
Spearman’s correlation coefficient, Kendall’s tao
Efficiency and properties of nonparametric tests
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1-
Nonparametric Statistical Methods.
Myles Hollander and Douglas A. Wolfe, 2nd Edition, 1999, John Wiley and sons, Inc.
2-
Applied Nonparametric Statistical Methods.
Peter Sprent and Nigel Charles Smelton, 3rd Edition, 2000, CRC Press.
3-
Practical Nonparametric Statistics.
W. G. Connover, 1999, 3rd Edition, Wiley Europe.
73
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 434
Generalized Linear Models
Course Information
Course Title: Generalized Linear Models
Course Number: STAT 434
Credit Hours: 3 (2+2)
Course Status: Major Elective Course
Prerequisite: STAT 322
Course Description
The Exponential family of distributions, Properties of distributions in the Exponential family, Generalized
linear models, Examples, Inference in Generalized Linear Models, Model Adequacy and Diagnostics,
The deviance statistic, The residuals, modifications of the residuals and model checks based on the
residuals. Special Cases of Generalized Linear Models, Normal theory linear models, Binary logistic
regression, Nominal and ordinal logistic regression, Poisson regression and Loglinear models.
Statistical software like Minitab, SPSS and R are used.
Course Objectives
The course aims at:
1-
Introducing generalized linear models as a generalization of the normal theory linear
models in certain directions
2-
Recognizing that many other commonly used models are special cases of generalized
linear models
3-
Familiarizing the student with the basic theory involved in inference from generalized
linear models
4-
Introducing model checking techniques suitable to geberalized linear models
5-
Developing the skills needed to handle practical situations with generalized linear
models..
6-
Stimulating interest to go for advanced studies in generalized linear models.
74
Learning Outcomes
By the end of this course, students will be able to:
12345-
Identify models that belong to generalized linear models
Prove and derive some of the basic results in generalized linear models
Perform statistical analysis for various types of data
Use computer packages effectively to analyze data from generalized linear models
Analyze data using logistic, poisson ordinal logistic and survival regression models and interpret the
results
6- Perform model checks and select the suitable model for a given data
Content Distribution
Week Topics
1
The Exponential family of distributions, Properties of distributions in the Exponential
family
2
Generalized linear models
3
Examples
4
Maximum likelihood estimation
5
The score vector and the information matrix
6
Large sample theory of the MLE
7
Large sample tests and intervals in Generalized Linear Models
8
The deviance statistic, The residuals, modifications of the residuals
9
Model checks based on the residuals
10
Normal theory linear models
11
Binary logistic regression
12
Nominal and ordinal logistic regression
13
Poisson regression and Loglinear models
14
Survival regression models
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1- Generalized Linear Models
Mc Cullagh, P., and Nelder, J., 2nd edition, 1989, Chapman & Hall
2- An Introduction to Generalized Linear Models.
Anette Dobson, 3rd edition, 2008, Chapman & Hall
3- An Introduction to Generalized Linear Models.
Dunteman and Ho, 1st edition, 2005, Sage Publications
75
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 442
Actuarial Statistics II
Course Information
Course Title: Actuarial Statistics II
Course Number: STAT 442
Credit Hours: 3 (2+2)
Course Status: Program Elective Course
Prerequisite: STAT 341
Course Description
Construction of Empirical Models, estimation for grouped and modified data, kernel density estimators.
Parametric Statistical methods, estimation and confidence intervals in actuarial models. Model Selection,
graphical methods, goodness of fit techniques. Credibility theory, Simulation of actuarial models, Case
study examples
Course Objectives
The course aims at:
1- Acquainting the student with methods of inference from complete and grouped data arising
from actuarial studies
2- Familiarising the student with likelihood and Bayesian methods in actuarial models
3- Introducing the student to model selection problems
4- Familiarising the student with the credibility theory applied to problems in actuarial statistics
5- Acquainting the student with the techniques of simulating actuarial models
Learning Outcomes
By the end of this course, students will be able to:
76
1- Conduct statistical inference based on complete, grouped, censored and modified data in the
actuarial studies
2- Work with actuarial bivariate models, copulas and models with covariates
3- Check the fit of models used in actuarial science using graphical methods and formal statistical tests
4- Apply the concepts of credibility theory in actuarial problems
5- Simulate actuarial models
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Construction of empirical models
Point estimation and confidence interval based on complete and grouped data
Inference based on modified data
Kernel density estimator, approximation for large data sets
Likelihood inference based on complete, grouped and censored samples
Bayesian inference in actuarial models
Estimation in bivariate models, Copulas
Models with covariates
Graphical methods for model selection
Goodness of fit tests, Kolmogorov-Smirnov test, Anderson Darling test, chi-square test
and Likelihood ratio test
Credibility theory, limited fluctuation credibility theory
Greatest accuracy credibility theory, empirical Bayes estimation in actuarial models
Simulation of actuarial models
Examples and Applications
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects.
References
1- Loss Models: From Data to Dicisions
Stuart A. Klugman, Harry, H. Panjer and Gordon E. Willmot, 3rd edition, Wiley InterScience.
2- Modern Actuarial Risk Theory
Rob Kaas, Marc Goovaerts, Jan Dhaene and Michel Denoit, 2nd edition, Springer.
3- Modern Actuarial Theory and Practice
Philip Booth, Robert Chadburn, Steve Haberman and Dewi James, 2nd edition, Chapman and
Hall/CRC
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COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 445
Reliability and Life Testing
Course Information
Course Title: Reliability and Life Testing
Course Number: STAT 445
Credit Hours: 3(2+2)
Course Status: Major Elective Course
Prerequisite: STAT 322
Course Description
Reliability Concepts; Component and System Reliability; Notions of Aging; Lifetime Distributions and
Hazard Functions; Types of Censoring; Nonparametric Estimation of Reliability Function; Kaplan-Meier
and Nelson Estimators; Parametric Inference Procedures for Exponential, Weibull and Extreme Value
Distributions; Proportional Hazards Regression Model; Accelerated Life Testing; Stress-Strength
Models. Statistical software like Minitab, SPSS and R are used.
Course Objectives
The course aims at:
1- Introducing censoring types and situations where censored data occur
2- Acquainting the student with lifetime distribution and the related functions like the reliability function,
the hazard function and the mean residual lifetime
3- Describing nonparametric inference with censored data
4- Acquainting the student with Parametric life distributions and the associated inference procedures
5- Describing regression with life data
6- Introducing the proportional hazards model
Learning Outcomes
By the end of this course, students will be able to:
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Analyze data from parametric life time distributions
Calculate and plot several characteristics of lifetime distributions
Check the goodness of fit based on possibly censored data
Conduct nonparametric tests and calculate confidence intervals and estimates
Analyze data from parametric regression models
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6- Conduct nonparametric regression methods and interpret the results
7- Analyze data from accelerated life tests
8- Use statistical software for reliability data analysis
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Introduction, types of censoring, examples
The reliability function and the related functions
Classes of life distributions, system lifetime
Parametric families of life distributions
Hazard functions, reliability functions and quantiles of specific
lifetime distributions
Parametric analysis of survival data
Applications
Nonparametric inference with censored data
Goodness of fit tests with censored data
Two sample problems
Applications
Regression with life data
The proportional hazards model
Accelerated life tests and related topics
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
1- Lifetime Data: Statistical Models and Methods,
Deshpande and Purohit.2006, world scientific publishing company
2- Statistical models and methods for lifetime data analysis
J. F. Lawless. 2nd edition, 2002, Wiley.
3- Statistical Methods for Reliability Data
W. Meeker and L. Escobar. Wiley, 1998
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COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 464
Environmental Statistics
Course Information
Course Title: Environmental Statistics
Course Number: STAT 464
Credit Hours: 3 (2+2)
Course Status: Major Elective Course
Prerequisite: STAT 312 and STAT 361
Course Description
Stochastic processes in the Environment. Fitting probability models to Environmental data. Tail
Exponential Method. Poisson Processes and its application. Negative binomial model (Contagion and
True Models). Capture-Recapture Method, Distance Sampling, Composite sampling, Introduction of
Rank Set sampling methods, adaptive cluster sampling and adaptive allocation methods.
Course Objectives
The course aims are:
1- To learn some statistical methods in Environmental Sciences.
2- To see the application of Statistics in Environmental and Ecological Sciences.
3- To train students who are familiar with some environmental statistics methods and have potential to
collaborate with Environmentalists.
Learning Outcomes
By the end of this course, students will be able to:
1- Fit statistical models to data from the environmental science.
2- Use some statistical techniques and models like the tail exponential method, the Poisson
process, the negative binomial model.
3- Calculate and apply certain types of distance measures
4- Apply and analyze the results from line transect sampling
5- Apply and analyze the results from ranked set sampling
6- Use adaptive cluster samples and adaptive allocation methods
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Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Introduction to remote senses and Stochastic processes in the Environment.
Fitting probability models to Environmental data. Tail Exponential method
Poisson Processes and its application. Negative binomial models (Contagion and
True Models).
Capture-Recapture: Peterson Method and sample size estimation. Schnabel
method
Confidence interval. Jolly-Seber Method. A catchability test
Distance sampling: Methods for spatial Maps. Nearest-Neighbor distance Method
Distances to second to the nth Nearest Neighbors
Indices of dispersion for Quadrat counts and distance measures
Line transect sampling and detection function.
Composite sampling: Classification, Extreme values
Estimating of prevalence. Cost functions
Rank set Sampling: Introduction of Rank Set sampling methods and its application
in Ecological problems,
Adaptive sampling: adaptive cluster sampling
Adaptive allocation methods.
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects.
References
1- Environmental Statistics and Data Analysis
Wayne R. Ott, 1995, CRC Press.
2- Ecological Methodology.
Krebs, C.J. 1999, 2nd edition, Benjamin Cummings.
3- Estimation of Animal Abundance.
Seber GAF, 2002, 2nd. Edward Arnold: London.
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COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 481
Multivariate Analysis
Course Information
Course Title: Multivariate Analysis
Course Number: STAT 481
Credit Hours: 3 (2+2)
Course Status: Program Compulsory Course
Prerequisite: STAT 322 and MATH 231
Course Description
The course discusses the analysis of multivariate data. Multivariate distributions and inference about
means are considered. Techniques like principal components, factor, cluster and discriminant analyses
were studied with examples. The use of computer packages is emphasized in this course. Real life data
are often used to illustrate the power and applicability of multivariate methods. Statistical software like
Minitab, SPSS and R are used.
Course Objectives
The course aims at:
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Enabling the students to organize multivariate data into an array and calculate its mean vector,
covariance matrix, and generalized variance.
Introducing the students to Multivariate Normal (MN) distribution and distribution of sample mean
and covariance from an MN distribution and the associated inferences.
Helping students acquire knowledge of principal components analysis (PCA) and Factor Analysis
(FA).
Introducing the elements of discriminant anlaysis and canonical correlation.
Familiarizing the students with the concepts of cluster analysis and multidimensional scaling.
Learning Outcomes
By the end of this course, students will be able to:
1- Calculate statistical quantities like the multivariate mean, covariance matrix and the generalized
variance.
2- Test hypotheses about the parameters of the multivariate normal distribution.
3- Compare several multivariate normal mean.
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Perform principal component analyses and factor analyses.
Apply the techniques of canonical correlation and discriminant analysis.
Apply the techniques of cluster analysis and multidimensional scaling.
Use statistical software for multivariate data analysis
Content Distribution
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
Multivariate Data: Summary Statistics
Multivariate Data: Plots
The Multivariate Normal Distribution
Inference about Single multivariate means
Inference about paired and independent multivariate means
One way Multivariate analysis of variance
Two way Multivariate analysis of variance
Examples and Discussion
Principal Components Analysis
Factor Analysis
Discriminant analysis
Canonical Correlation
Cluster Analysis
Examples
Assessment: Midterm Exams, Final Exam, Assignments, Mini Projects, Lab assignments.
References
4- Applied Multivariate Statistical Analysis
Richard A. Johnson and Dean W. Wichern, 6th edition, 2007, Prentice Hall.
5- Multivariate Statistical Methods: A Primer
Bryan Manly, 3rd edition, 2004, Chapman & Hall/CRC.
3- Methods of Multivariate Analysis
A. C. Rencher, 2nd edition, 2002, John Wiley and sons, Inc.
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COLLEGE OF ARTS AND SCIENCES
DEPARTMENT of MATHEMATICS, STATISTICS AND PHYSICS
STAT 482
Bayesian Statistics
Course Information
Course Title: Bayesian Statistics
Course Number: STAT 482
Credit Hours: 3 (2+2)
Course Status: Major Elective Course
Prerequisite: STAT 322
Course Description
Nature of Bayesian Statistics, Prior and posterior distributions. Noninformative priors. Jeffereys rule.
Conjugate priors. Bayesian Inference, Quadratic loss function and Bayes estimators, Highest posterior
density intervals, Bayesian tests of hypothesis. Bayesian methods in the normal and some other
distributions. Approximate Bayesian Methods, Asymptotic approximations of the Bayes estimator, The
Lindley and Tierney-Kadane methods, Markov chain Monte Carlo methods and the Gibbs sampler.
Course Objectives
The course aims are:
1- To introduce the basic concepts and principles of Bayesian inference.
2- To give the students some standard normal theory results from a Bayesian perspective and to
contrast them with the classical approach to inference.
3- To Acquaint students with methods of developing Bayesian inference procedures.
4- To introduce the students to the approximations usually used in Bayesian inference to solve the
high dimensional integrations usually faced in Bayesian methodology.
Learning Outcomes
By the end of this course, students will be able to:
1- Construct and find suitable non informative and conjugate prior distributions
2- Calculate Bayes estimator and Bayes intervals, in particular, the highest posterior density
intervals
3- Apply Bayesian methodology to some standards problems like the one and two sample
normal theory situations
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4- Use asymptotic approximations to Bayesian Estimators like Tierney Kadane and Laplace
methods
5- Apply Markov chain Monte Carlo methods and Gibbs sampler techniques of computer
intensive Bayesian calculations
Content Distribution
Week
1
2
Topics
Probability and Bayes theorem, Examples on Bayes theorem.
Parameters as random variables. Prior distributions
3
4
5
Noninformative priors. Jeffereys rule. Conjugate priors
Posterior distributions
Quadratic loss function and Bayes estimators
6
7
Highest posterior density intervals
Bayesian tests of hypothesis
8
9
10
11
12
The normal one and two-sample location problems
The Behrens-Fisher problem. The variance and ratio of variances
Asymptotic approximations of the Bayes estimator
The Lindley and Tierney-Kadane methods
Markov chain Monte Carlo methods
13
14
Gibbs sampler
Applications
Assessment: Midterm Exams, Final Exam, Assignments, Quizzes.
References
1- Bayesian Statistics: An Introduction.
Peter M. Lee, 3rd Edition, 2004, Arnold.
2- Introduction to Bayesian Statistics.
Bolstad, 2nd Edition, 2007, Wiley
3- Bayesian Data Analysis.
Carlin, Stern and Rubin, 2nd edition, 2003, Chapman and Hall/CRC
85
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS, STATISTICS AND PHYSICS
STAT 499
Graduation Project
Course Information
Course Title: Graduation Project
Course Number: STAT 499
Credit Hours: 3
Course Status: Major Compulsory Course
Prerequisite: Approval of the Department Head
Course Description
This project is a final project in which graduating students demonstrate their ability to design
questionnaires, conduct surveys and/or retrieve information from the internet, analyze the
collected data using various techniques, interpret the results, present what they have
accomplished to an audience in a concise manner and reflect on their experience. The
Graduation Project provides students the opportunity to relate content knowledge and acquired
skills to real world situations and issues.
Course Objectives
The course aims at:
1- Introducing the student to the field of working with real data
2- Familiarizing the student with the methods of collecting real data and the difficulties associated with
them
3- Acquainting the student with the methodology of model building and data analysis
4- Training the student on how to interpret the results of real life studies
5- Familiarizing the student with the general methodology of research and the reporting of results
6- Training the student on oral presentation of his findings
Learning Outcomes
By the end of this course, students will be able to:
1- Formulate a data analysis problem in a statistical framework.
2- Use perfectly at least one statistical software package to analyze data.
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3- Use a variety of methods for exploring, summarizing and presenting data.
4- Apply statistical models and methods to solve practical problems.
5- Interpret the results of a statistical analysis.
6- Comment critically on choices of model and method of analysis.
7- Communicate the results of statistical investigations and data analyses, using a form, structure and
style that suit the purpose.
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