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#### Admissions Announced for BS/BS 5th Semester/Certificate/Diploma/M.Phil/MS & Ph.D Programs (Admissions Fall 2021) Downloads Online Results Jobs & Careers Degree Verification Tenders Central Library Semester Rules UOH Statutes 2016

### Department of Mathematics and Statistics

#### Course Outlines for BS Statistics

LIST OF GENERAL COURSES FOR STATISTICS

Seven courses are to be selected from the following list of courses, according to available facilities and faculty of the universities.

• Human Resource Management
• Environmental Sciences
• Principles of Management & Marketing
• Basic Financial Management
• History of Human Civilization
• Introduction to Biology
• Foreign Language other than English
• Introduction to Physics
• Introduction to Genetics
• Introduction to Geography

or any other subject depending upon the expertise available.

Elective Courses for BS (4-Year) Programme for Statistics

• Operations Research
• Stochastic Process
• Reliability Analysis
• Decision Theory
• Robust Methods
• Survival Analysis
• Bio-Statistics
• Data Mining
• Actuarial Statistics-I
• Actuarial Statistics-II
• Mathematical Models and Simulation
• Categorical Data Analysis
• Numerical Methods
• Bayesian Inference
• Statistical Quality Control,

or any other subject depending upon the expertise available.

DETAIL OF COURSES

The proposed outlines of the BS (4-YEAR) programme in Statistics are as follows:

STAT- 101:         Introductory Statistics

Learning Objectives:

• To have introduction of statistics as a field of knowledge and its scope and relevance to other disciplines of natural and social sciences.
• To equipped and prepare students for advance courses in the field of statistics.
• To achieve the capability of critical thinking about data and its sources; have idea about variables and their types and scale measures.
• Be able to calculate and interpret descriptive statistics (able to classify, tabulate, describe and display data using software).

Learning Outcomes:

• Acquire the basic knowledge of the discipline of Statistics.
• Understand and differentiate between the types of data and variables.
• Evaluate and Interpret basic descriptive statistics. Display and Interpret data graphs.

Course Contents:

The nature and scope of the Statistics, Variables and their types, Data and its sources, Scales of measurements, Tabulation and classification of data, Graphs and Charts: Stem-and leaf diagram, Box and Whisker plots and their interpretation. Measures of Central Tendency, Quantiles, Measures of Dispersion: Their properties, usage, limitations and comparison. Moments, Measures of Skewness and Kurtosis and Distribution shapes. Rates and ratios, Standardized scores.

Index numbers: construction and uses of index numbers, un-weighted index numbers (simple aggregative index, average of relative price index numbers), weighted index numbers (Laspayer’s, Paasche’s and Fisher’s ideal index numbers), Consumer price index (CPI) and Sensitive Price Indicators

Recommended Books:

• Clarke, G. M., & Cooke, D. (1978). A basic course in statistics (No. 519.5 C53).
• Chaudhry, S.M. and Kamal, S. (2008), “Introduction to Statistical Theory” Parts I & II, 8th ed, Ilmi Kitab Khana, Lahore, Pakistan.
• Mann, P. S. (2010) Introductory Statistics. Wiley.
• Spiegel, M.R., Schiller, J.L. and Sirinivasan, R.L. (2000) “Probability and Statistics”, 2nd ed. Schaums Outlines Series. McGraw Hill. NY.
• Walpole, R.E., Myers, R.H and Myers, S.L. (1998), “Probability and Statistics for Engineers and Scientist” 6th edition, Prentice Hall, NY.
• Zaman, A. (2016), “Introduction to Statistics” Online access for book and related data sets. (https://sites.google.com/site/introstats4muslims/excel).

STAT- 102:         Introduction    to    Probability    &    Probability Distributions

Learning Objectives:

• Understand    basic   concepts   of   probability,   conditional   probability, independence etc.
• Be familiar with some of the more commonly encountered random variables, particularly the Binomial and Normal random variable.
• Be able to calculate first two moments of common random variables i.e. means and variances.
• Be able to apply the concepts of random variables to scientific applications. Computation of uncertainty using probability techniques.
• Learning Outcomes:

• Acquire the basic knowledge of probability and probability distribution.
• Understand the concepts of basic techniques of measuring the uncertainty problem.
• Analyze the problem of genetics finance and telecommunications by using probability techniques.
• Course Contents:

Set theory and its operations, Probability Concepts, Addition and Multiplication Rules, Bivariate Frequency Tables, Joint and Marginal Probabilities, Conditional Probability and Independence, Bayes’ Rule. Random Variables, Discrete Probability Distribution, Mean and Variance of a Discrete Random Variable, Bernoulli Trials, Properties, Applications and Fitting of Binomial, Poisson, Hypergeometric, Negative Binomial and Geometric Distributions. Continuous Random Variable, Probability Density Function and its Properties, Normal Distribution and its Properties, Standard Normal Curve.

Recommended Books:

• Cacoullos,   T.   (2012). Exercises   in   probability.   Springer   Science   & Business Media.
• Mclave, J.T., Benson, P.G. and Snitch, T. (2005) “Statistics for Business & Economics” 9th Edition. Prentice Hall, New Jersey.
• Santos, David (David A.) (2011). Probability : an introduction. Jones and Bartlett Publishers, Sudbury, Mass
• Walpole, R.E., Myers, R.H and Myers, S.L. (2007), “Probability and Statistics for Engineers and Scientist” 7th edition, Prentice Hall, NY.

STAT- 202:         Basic Statistical Inference Learning Objectives:

• To understanding of basic techniques of sampling and estimation, their

properties and application

• To select a sample from a given population and use it to make inferences about the population and its parameter
• To test, deduce and infer the validity of different types of hypotheses and models built on the basis of the raw data collected in diverse problem- situations.

Learning Outcomes:

• Acquire the knowledge of the sampling distributions and their properties.
• Derive the appropriate estimators for parameters using best estimation procedure.
• Use appropriate sampling distributions for interval estimation and hypotheses testing.
• Apply   appropriate    inferential   procedures   to   handle    the   practical situations.

Course Contents:

Sampling and sampling distribution of sample mean, proportion, difference between means and difference between proportions; Point and interval estimate properties of good point estimator; Testing of hypothesis for population mean, difference between population means and population proportion and difference between two population proportions, difference between means for paired data; Single population variance, ratio of two variances; Non-parametric methods: The sign test, Wilcoxon’s signed rank test, Mann-Whitney U test, Median test, Run test, Kolmogrorov-Smirnov test, Kruskal-Wallis test, Median test for k-samples, Friedman test.

Pre-Requisite- STAT-102

Recommended Books:

• Ross, S. (2017). A first course in Probability. 9th edition. Pearson Education Limited.
• DeGroot, M. Schervish, M. (2017). Probability and Statistics. 4th edition. Pearson Education Limited.
• Srivastava,   M.K.,   Khan,   A.H.   and   Srivastava, N.  (2014).    Statistical Inference: Theory of Estimation. Prentice-Hall of India Pvt. Ltd
• Clark, G.M. and Cooke, D. (1998). A Basic Course in Statistics. 4th ed, Arnold, London.
• Mclave, J.T., Benson P.G. and Sincich, T. (2014). Statistics for Business and Economics. 12th Edition. Pearson Education Ltd, U.K.
• Spiegel, M.R., Schiller, J.L. and Sirinivasan, R.L. (2015). Probability and Statistics. 3rd edition. Schaums Outlines Series. McGraw-Hill. NY.

STAT-204           Linear Algebra

Course Objectives:

• To develop the ability to solve problems using the techniques of linear algebra
• To Understand Euclidean vector spaces, their inherent arithmetic and algebraic structure, and the accompanying geometry that arise
• Acquire    facility    working    with    general    vector    spaces,    linear transformations, coordinate vectors, and the changing of bases.
• To analyze the structure of real-world problems and plan solution strategies. Solve the problems using appropriate tools.

Learning Outcomes:

• Interpret the Use of    vector equations and linear transformations and its application in image processing and Control theory, etc
• Apply mathematical concepts in problem-solving through integration of new material and modeling
• Analyze/interpret quantitative data verbally, graphically, symbolically and numerically.

Course Contents:

Linear Equations: Introduction, Gaussian elimination and matrices, Gauss- Jordan method, Making Gaussian elimination work, Ill-conditioned systems. Echelon Forms: Row echelon form and rank, The reduced row echelon form, Consistency of linear systems, Homogeneous systems, Nonhomogeneous systems. Matrix Algebra: Addition, scalar multiplication and transposition, linearity, matrix multiplication, properties of matrix multiplication, matrix inversion, inverses of sums and sensitivity, elementary matrices and equivalence, The LU factorization. Vector spaces: spaces and subspaces, four fundamental subspaces, linear independence, basis and dimension, more about rank, classical least squares, linear transformations, change of basis and similarity, invariant subspaces. Norms, Inner products, and Orthogonality: Vector norms and inner products, orthogonal vectors, Gram-Schmidt procedure, Unitary and orthogonal matrices, orthogonal reduction, complementary subspaces, range-null space decomposition, orthogonal decomposition, singular value decomposition, orthogonal projection, angles between subspaces. Determinants and their properties. Eigenvalues and Eigenvectors.

Recommended Books:

• Anton, H. (2013). Elementary Linear Algebra, John Wisely publisher, 10th edition,
• David C. L. (2014). Linear Algebra and its Applications, 5th edition.
• Leon, J. S. (2015). Linear Algebra with Applications, 9th edition.
• Seymour, L and Marc, L. (2006), Linear Algebra, Schaum’s Outline Series, McGraw-Hill.
• Strang, G. (2016). Introduction to Linear Algrebra , 5th edition.

STAT- 203:         Introduction  to  Regression   and   Analysis  of Variance

Course Objectives:

• To provide foundations of regression analysis.
• To provide basic knowledge and art of statistical data analysis
• To predict and draw inference about the parameters of the parameters of population.
• Learning Outcomes:

• Explore more adequately the connection between theory of regression.
• Analysis of real world problems.
• Prediction of dependent variable.
• Course Contents:

Relationship between variables, Simple linear regression model, Estimation of parameters by method of least squares and corresponding variance estimates, Testing and confidence intervals for least squares estimators, mean prediction and individual prediction. Multiple linear regression with two regressors, coefficient of multiple determination, Partial and multiple correlation up to three variables. Inference of simple, partial and multiple correlation coefficients, Analysis of variance for one-way classification and two-way classification. Decomposition of total sum of squares, Multiple comparison tests; least significant difference and Duncans multiple range test, Tukey test and Least significant difference test.

Pre-Requisite: STAT-101

Recommended Books:

• Montgomery, D. C., Peck, E. A., and Vining, G. G. (2012). Introduction to linear regression analysis (Vol. 821). John Wiley and Sons.
• Dielman, T. E. (2001). Applied regression analysis for business and economics. Pacific Grove, CA: Duxbury/Thomson Learning.
• Rawlings, J. O., Pantula, S. G., and Dickey, D. A. (2001). Applied regression analysis: a research tool. Springer Science and Business Media.

STAT-401:          Exploratory  Data   Analysis  and  Visualization (EDAV)

Learning Objectives:

• to provide solid understanding of the process of Exploratory Data Analysis
• to educate students in data exploration, analysis, and visualization
• to train students in industry standard tools for data analysis and visualization
• Learning outcomes:

• describe exploratory data analysis and visualization concepts
• describe data analysis and visualization models and algorithms
• describe applicability of different data analysis and visualization models techniques to solve real-world problems
• acquire and pre-process data
• apply exploratory data analysis to some real data sets and provide interpretations via relevant visualization
•

Course Contents:

Exploratory Data Analysis: Explore, Visualize, Analyze, Repeat. Selective data collective and data exploration. Data visualization and Data analysis (using Excel/Tableau/R/STATA/SPSS etc).

Recommended Books:

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STAT- 204: Statistical Packages

Course Objectives:

• To understand basics of data analysis through Minitab, SPSS and R.
• To learn visualization   of data through Minitab, SPSS and R.
• To learn basic programming in R.
•

Learning Outcomes:

• Understand the data presentation and analysis using Minitab and SPSS.
• Learn basic programming in R for statistical data analysis.
• Describe concepts as they are implemented in real world data.
• Course Contents:

Introduction to statistical packages and programming languages, Introduction to Minitab, data manipulation, graphical representation, qualitative and quantitative data analysis and programming.

Introduction to SPSS, data manipulation, descriptive statistics, function related to probability distributions, SPSS modules, graphical representation of data, tabulation and transformation of variables.

Introduction to R, language essentials; expression and objects, functions and arguments, vectors, missing values, matrices and arrays, factors, data frames, indexing, conditional selection, indexing of data frames, sorting, Data entry; reading from text files, the data editor, interfacing to other programs. Descriptive statistics and graphics.

Note: Use of any other statistical package based upon the availability of the Software.

Recommended Books:

• Ryan, B. F. and Joiner, B. L. (2001). Minitab handbook. Duxbury Press.
• Holmes,  W. H. and    Rinaman, W. C. (2014). Introduction to SPSS. In Statistical Literacy for Clinical Practitioners (pp. 25-57). Springer, Cham.
• Dalgaard, P. (2002) Introductory Statistics with R, Springer,
• Verzani, J. (2005). Using R for Introductory Statistics, Chapman and Hall/ CRC press, Taylor and Francis.

STAT- 301:         Probability Distributions- I

Course Objectives:

• This course is designed to give students a conceptual knowledge of discrete random variables and probability theory.
• This course provides the fundamentals of probability theory in different disciplines.
• This course helps to model the uncertain behavior from the real life scenario.

Learning Outcomes:

• Understand the basic concepts and applications of probability.
• Investigate the nature of stochastic process and apply suitable probability distributions for the random variable generated from such process.
• Find probabilities using probability distributions.
• Use probability concepts and laws in decision analysis.

Course Contents:

Distribution function, Probability mass and density functions. Location, scale, and shape parameters. Joint and conditional distributions for two and more random variables, Marginal and conditional distributions, stochastic independence, Mathematical expectation and its properties, Conditional expectation, variance and moments, Probability generating, Moment generating and characteristic functions with their properties. Factorial Moments, Cummulants, L moments and their relationships. Probability distributions: Bernoulli, Binomial, Hypergeometric, Poisson, Negative binomial, Geometric, discrete uniform, Multinomial distribution. Normal approximation to binomial, Poisson and Hypergeometric distribution.

Pre-Requisite: STAT-102

Recommended Books:

• Casella, G. and Berger, R.L. (2008). Statistical Inference, Cengage Learning, New York, USA.
• Hirai, A.S. (2002), A Course in Mathematical Statistics, Ilmi Katab Khana, Lahore.
• Hogg,   R.M.,   McKean,   J.   and   Craig,   A.T.   (2013).    Introduction   to Mathematical Statistics. Prentice Hall, New Jersey, USA.
• Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, John Wiley & Sons, New York, USA.
• Johnson, N.L., Kotz, S. and Kemp, A.W. (1993). Univariate Discrete Distributions, John Wiley & Sons, New York, USA.
• Mood, A.M, Graybill, F.A. and Boes, D.C. (2007). Introduction to the Theory of Statistics, McGraw Hill, New York, USA.
• STAT- 303:         Sampling Techniques-I

Course Objectives:

• To introduce the concept and scope of sampling.
• To determine the sample size for conducting a survey.

• <
• To learn ratio and regression estimations.
• To understand the concept of simple and stratified random sampling techniques.

Learning Outcomes:

• Use and implement of sampling designs.
• Apply the simple random sampling and the stratified random sampling appropriately in real world problems.
• Estimate the population parameters by using simple and stratified random sampling techniques.

Course Contents:

Introduction of Sampling, advantages of sampling, requirements of a good sample, bias, sampling and non-sampling errors, Steps and problems involved in planning and conduct of census and their sources, sample surveys, Selection and estimation procedures. Description and properties of simple random sampling, Sampling for proportions and percentages, Estimation of variances, standard errors and confidence limits, Sample size determination under different conditions, Description and properties of stratified random sampling, Formation of strata, Different methods of allocation of sample size, Ratio and regression estimates in simple and stratified random sampling

Pre-Requisite:   STAT-201

Recommended Books:

• Bethelem, J. (2009). Applied Survey Methods: A Statistical Perspective. Wiley.
• Cochran, W.G. (1977). Sampling Techniques. John Wiley and Sons, 3rd ed, New York.
• Des Raj and Chandhok P. (1998). Sample Survey Theory. Narosa Publishing House, New Delhi.
• Kish, L. (1992). Survey Sampling. John Wiley, New York.
• Singh, R. and Singh N, (1996). Elements of Survey Sampling. Kulwar, Dodrecht.

and
*Various publications of Pakistan Bureau of Statistics (PBS).

STAT- 307:         Regression Analysis

Course Objectives:

• To understand the basic assumptions of regression analysis.
• To handle the problems arising from the violation of assumptions.
• To understand the estimation techniques of parameters.
• To give the concept of nonlinear regression analysis.
• <

Learning Outcomes:

• Students would have enough knowledge of regression analysis.
• Students will be able to understand the concept of basic assumption of regression and how to overcome these problems.
• It developed the skills of students to analyze the real phenomena of regression models.

Course Contents:

Linear regression and its assumptions, Least squares estimators, Maximum Likelihood Estimator, tests of significance for regression model and regression parameters. Confidence interval for regression parameters, Test of linearity of regression, Use of extraneous information in linear regression model. Residual analysis, Detection and study of outliers and influential observations, Polynomial regression, orthogonal polynomial, orthogonal regression analysis and Specification of models

Pre-Requisite:   STAT-203

Recommended Books:

• Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to linear regression analysis (Vol. 821). John Wiley and Sons.
• Rawlings,  J.  O.,  Pantula,  S.  G.,  and     Dickey, D. A. (2001). Applied regression analysis: a research tool. Springer Science & Business Media.
• Dielman, T. E. (2001). Applied regression analysis for business and economics. Pacific Grove, CA: Duxbury Thomson Learning.
• Yan, X. and Zu, X. G. (2009) Linear Regression Analysis: Theory and Computing. World Scientific Publications.

STAT- 305:         Design and Analysis of Experiments-I

Course Objectives:

• This course provides the fundamentals of experimental designs and their uses in different disciplines.
• To provide basic and advanced learning of investigation for conclusions through planning and designing of experiments.
• To train students through innovative instruction in design theory and methodology that will help them in addressing the significance of experimental design in statistics and across the universal disciplines.
•

Learning Outcomes:

• Understand the basic concepts and applications of experimental design.
• Decide appropriate design for given scenario.
• Analyze the data generated from different designs and interpret the results.
• <

Course Contents:

Introduction to experimental design and its terminology; Planning and designing of experiment and research; Aspects of experimental design, basic principles of experimental design, fixed and random effects. Analysis of variance, estimation of model parameters. Checking model adequacy, Inference beyond ANOVA multiple comparisons, Contrast analysis, orthogonal polynomial contrasts and trend analysis. Basic experimental designs; completely randomized design, randomized complete block design and Latin square design. Relative efficiency of these designs. Incomplete block designs (IBD), balanced incomplete block designs (BIBD) and partially balanced incomplete block designs (PBIBD). Intra-block and Inter-block analysis of IBD.

Pre-Requisite:   STAT-203 Recommended Books:

• Gomez,   K.A.   and   Gomez,   A.A.   (1984).   Statistical   Procedures   for

Agricultural Research, John Wiley & Sons, New York, USA.

• Kehul, R.O. (2000). Design of Experiments: Statistical Principles of Research Design and Analysis, Duxbury/ Thomson Learning, New York, USA.
• Montgomery, D.C. (2012). Design and Analysis of Experiments, John Wiley & Sons, New York, USA.
• Oehlert, G.W. (2000). A first course in design and analysis of experiments,

W.H. Freeman, New York, USA.

• Steel, R.G.D, Torrie , J.H. and Dickey D.A. (2008). Principles and Procedures of Statistics: A Biometrical Approach. McGraw-Hill, Michigan, USA.

STAT- 310:         Non-Parametric Methods

Rationale of non-parametric methods, Chi-Square Procedures: Chi-Square Goodness of fit Test, Chi-Square test of independence, Location estimates for single sample: The sign test, modified sign test, Wilcoxon signed rank test, confidence interval based on these tests. Runs test for randomness. Anderson- Darling test.

Distribution tests and rank transformation, Kolmogrov’s test, Lilliefor’s test and Shapiro-Wilks test for normality. Tests and estimation for two independent samples; the median test, Wilcoxon Mann – Whitney test. The Siegel – Tukey test, the squared rank test for variance, Smirnov test, Tests for paired samples, Kruskal – Wallis test, Friedman test, multiple comparison with the Friedman test, Cochran’s test for binary responses Spearman’s rank correlation coefficient, Kendall’s rank correlation coefficient. Theil’s regression method

Pre-Requisite: STAT-202

Recommended Books:

• Conover, W.J. (1999), Practical Nonparametric Statistics, 3rd Edition, John Wiley and Sons, New York
• Gibbons, J.D. and Chakraborti, S. (1992), Nonparametric Statistical Inference, Marcel Decker, New York.
• Lehman, E.L. (1973), Nonparametric Statistical Methods, based on Ranks, Holden-Day San Francesco
• Maritz, J.S. (1995). Distribution-Free Statistical Methods, Chapman & Hall London
• Sprint, P. (2007). Applied Nonparametric Statistical Methods, 4th edition, Chapman & Hall London

STAT- 302:         Probability Distributions - II

Course Objectives:

• This course is designed to give students a conceptual knowledge of continuous random variables and probability theory.
• This course provides the fundamentals of probability theory in different disciplines.
• This course helps to model the uncertain behavior from the real life scenario.

Learning Outcomes:

• Understand the basic concepts and applications of probability.
• Investigate the nature of stochastic process and apply suitable probability distributions for the random variable generated from such process.
• Find probabilities using probability distributions.
• Use probability concepts and laws in decision analysis.

Course Contents:

Overview of the continuous random variables, Uniform, Beta, Lognormal, Exponential, Gamma, Laplace, Rayleigh and Weibull distributions with their properties; Bivariate Normal distribution and its properties, Distributions of functions of random variables: Chi-square, t and F distributions, their derivations and properties. Central limit and Chebyshev's theorems, Weak and Strong Laws of large numbers and their applications, Order statistics, Distributions of r-th and s-th order statistics.

Pre-Requisite: STAT-301 Recommended Books:

• Casella, G. and Berger, R.L. (2008). Statistical Inference, Cengage

Learning, New York, USA.

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• Hirai, A.S. (2002), A Course in Mathematical Statistics, Ilmi Katab Khana, Lahore.
• Hogg,   R.M.,   McKean,   J.   and   Craig,   A.T.   (2013).   Introduction   to Mathematical Statistics. Prentice Hall, New Jersey, USA.
• Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, John Wiley & Sons, New York, USA.
• Johnson, N.L., Kotz, S. and Kemp, A.W. (1993). Univariate Discrete Distributions, John Wiley & Sons, New York, USA.
• Mood, A.M, Graybill, F.A. and Boes, D.C. (2007). Introduction to the Theory of Statistics, McGraw Hill, New York, USA.

STAT- 304:         Sampling Techniques-II

Course Objectives:

• To  understand  the  concept  of  systematic,  cluster,     multistage and multiphase sampling techniques.
• Comparison among different sampling techniques.
• To learn ratio and regression estimations.
• To understand the non-response, their sources, and randomized response technique.

Learning Outcomes:

• Use and implement of systematic and cluster sampling designs.
• Apply the multistage and multiphase sampling appropriately in real world problems.
• Estimate the population parameters by using systematic and cluster sampling techniques.

Course Contents:

Systematic sampling, Cluster Sampling. Efficiency of systematic sampling compared with simple random sampling, stratified random sampling and cluster sampling. Sub sampling, proportion to size (PPS)-Sampling, Double Sampling, Multistage and Multiphase sampling, Thomson Hurwitz estimator, Comparison of different sample designs; non-response, their sources and bias and Randomized response.

Note: Practical’s of this course shall include visits of the students to various national statistical organizations and a report submitted to this effect.

Pre-Requisite:   STAT-303

Recommended Books:

• Bethelem, J. (2009). Applied Survey Methods: A Statistical Perspective. Wiley.
• Cochran, W.G. (1977). Sampling Techniques. John Wiley and Sons, 3rd ed, New York.
• Des Raj and Chandhok P. (1998). Sample Survey Theory. Narosa Publishing House, New Delhi.
• Kish, L. (1992). Survey Sampling. John Wiley, New York.
• Singh, R. and Singh N, (1996). Elements of Survey Sampling. Kulwar, Dodrecht.
##### *Various publications of Pakistan Bureau of Statistics (PBS).

STAT- 308:         Econometrics

Course Objectives:

• The purpose of this course is to introduce students to the main concepts and tools used in econometrics.
• In particular, to learn when and how to apply regression analysis. Learn the basic assumptions and techniques used to run estimations and make inferences in the context of a linear equation framework.
• To learn to recognize specification and data problems. Also additional tools to handle time series data.
• Each topic will be approached with a mix of intuitive explanations, theoretical characterization and proofs.
• And practical applications, including interpretation of regression output.
• Learning outcomes:

• Conduct basic statistical and econometric analysis. Explain and interpret econometric results.
• Explain    econometric    concepts    and     results     intuitively, conduct independent data analysis and inquiry using the tools of statistics and econometrics.
• Conduct Research with econometrics, derive econometric results mathematically
• Course Contents:

Introduction to econometrics, Problems of autocorrelation, multicollinearity, heteroscedasticity and their solution; Ridge regression, Lagged variables, Autoregressive models. Dummy variables, Errors in Variables, Instrumental variables, System of simultaneous linear equations, Identification-Estimation method, indirect and two-stage least squares methods, restricted least squares. Test of identifying restrictions; Estimation with stochastic regressor, generalized least squares estimators.

Recommended Books:

• Baltagi, B. H. (1999). “Econometrics”, 2nd Edition, Springer Varlog.
• Draper, N.R. and Smith, H. (2004). “Applied Regression Analysis”, John Wiley, New York.
• Gujrati, D. (2004). “Basic Econometrics”, John Wiley, New York.
• Koutsoyiannis, A. (1980), “Theory of Econometrics”, Macmillan.
• Wonnacot, T.H. and Wonnacot R.J. (1998). “Econometrics”, John Wiley, New York

STAT- 306:         Design and Analysis of Experiments-II

Course Objectives:

• This course provides the advanced knowledge of experimental designs and their uses in different disciplines.
• To provide basic and advanced learning of investigation for conclusions through planning and designing of experiments.
• To train students through innovative instruction in design theory and methodology that will help them in addressing the significance of experimental design in statistics and across the universal disciplines.

Learning Outcomes:

• Understand the basic concepts and applications of experimental design.
• Decide appropriate design for given scenario.
• Analyze the data generated from different designs and interpret the results.

Course Contents:

Introduction to factorial experiments, simple, main and interaction effects. Hidden replication. 2k and 3k series and mixed level factorial experiments and their analysis. Analysis of Covariance (ANCOVA). Confounding in factorial experiments, complete and partial confounding; Single replication of factorial experiments. Fractional factorial experiments. Introduction of response surface methods; first and second order designs, central composite designs, fitting of response surface models and estimation of optimum response, split plot design and its variations.

Pre-Requisite:   STAT-305 Recommended Books:

• Gomez,   K.A.   and   Gomez,   A.A.   (1984).   Statistical   Procedures   for

Agricultural Research, John Wiley & Sons, New York, USA.

• Kehul, R.O. (2000). Design of Experiments: Statistical Principles of Research Design and Analysis, Duxbury/ Thomson Learning, New York, USA.
• Montgomery, D.C. (2012). Design and Analysis of Experiments, John Wiley & Sons, New York, USA.
• Oehlert, G.W. (2000). A first course in design and analysis of experiments, W.H. Freeman, New York, USA.
• Steel, R.G.D, Torrie , J.H. and Dickey D.A. (2008). Principles and Procedures of Statistics: A Biometrical Approach. McGraw-Hill, Michigan, USA.

STAT- 311:         Population Studies

Meaning of vital statistics, registrations of Birth and death in Pakistan. Uses of vital statistics, short comings of vital statistics, rates and ratios (Sex ratio, child women ratio, birth and death ratio, population growth rate, classification of natal rates, death rates or mortality rates, crude death rate, specific death rate, infant mortality rate, case fatality rate, fertility rates, crude birth rate, specific birth rate, standardized death rate, reproduction rates, morbidity or sickness rates, marriage rates, divorce rates etc. general; fertility rate, total fertility rate). Basic concepts of demography, Sources of demographic data: The population and housing census, Registration of vital events. Demographic surveys, Components of population growth, composition of population and vital events, Types and sources of errors, Data quality testing procedures, testing the accuracy of age and sex distribution, Fertility and mortality measures, Estimation from incomplete Data

Construction of complete and abridged life tables, Different types of life tables, Graphs of lx, qx and ex, Description and uses of life table columns.

Recommended Books:

• Bogue, D.J. Arriagu, E.E., Anderson, D.L. (1993), “Readings in Population Research Methodology”, Vol. I-VIII, United Nations Fund; Social Development Centre, Chicago.
• Hinde, A., (1998). “Demographic Method”, Arnold New York.
• Impagliazo,     J.    (1993),     Deterministic    Aspects    of    Mathematical Demography, Springer Verlag New York.
• Jay Weinstein, Vijayan, K. Pillai, (2001) “Demography: The Science of Population”. Allyn & Bacon.1.
• Keyfitz, N. (1983) “Applied Mathematical Demography”, Springer Verlag N.Y.
• Palmore, J.A; Gardner, R.W. (1994), “Measuring Mortality Increase”; East West Centre, Honolulu.
• Pollard,   A.H.,   Yousaf,   F   &   Pollard,    G.M.   (1982),    “Demographic Techniques”, Pergamon Press, Sydney.
• Rukanuddin A.R. and Farooqi, M.N.I.., (1988), “The State of Population in Pakistan – 1987”, NIPS, Islamabad.
• Govt. of Pakistan (1998), National, Provincial and District census reports and other supplementary reports with respect to 1998 census; PCO, Islamabad.
• Pakistan Demographic Survey (2007), Govt. of Pakistan.
• Publications of population census organizations.
• United Nations (1990), “World Population Monitoring 1989”, UNFPA.
• United Nations (1998), “World Population Assessment”, UNFPA; New York.
• United Nations (1996), “Added years of Life in Asia”, ESCAP; U.N., Thailand.
• Haupt, A., Kane, T. T., and Haub, C. (2011) PRB’s Population Handbook.

STAT- 312:         Population Models
Stationary population models, Population estimates and projections, Inter- censual estimates, Population projections through various methods. Theory of demographic transition, Stable and stationary population models, their applications and uses, Malthusian and post Malthusian theories of growth, Consequences of world population growth & population explosion; State of Population in Pakistan, Development of demographic profile in Pakistan, Recent demographic parameters. Current and future demographic activities in Pakistan

Recommended Books:

• Bogue, D.J. Arriagu, E.E., Anderson, D.L. (1993), “Readings in Population Research Methodology”, Vol. I-VIII, United Nations Fund; Social Development Centre, Chicago.
• Hinde, A., (1998). “Demographic Method”, Arnold New York.
• Impagliazo,     J.    (1993),     Deterministic    Aspects    of    Mathematical Demography, Springer Verlag New York.
• Jay Weinstein, Vijayan, K. Pillai, (2001) “Demography: The Science of Population”. Allyn & Bacon.1.
• Keyfitz, N. (1983) “Applied Mathematical Demography”, Springer Verlag N.Y.
• Palmore, J.A; Gardner, R.W. (1994), “Measuring Mortality Increase”; East West Centre, Honolulu.
• Pollard,    A.H.,   Yousaf,   F   &   Pollard,   G.M.   (1982),    “Demographic Techniques”, Pergamon Press, Sydney.
• Rukanuddin A.R. and Farooqi, M.N.I.., (1988), “The State of Population in Pakistan – 1987”, NIPS, Islamabad.
• Govt. of Pakistan (1998), National, Provincial and District census reports and other supplementary reports with respect to 1998 census; PCO, Islamabad.
• Pakistan Demographic Survey (2007), Govt. of Pakistan.
• Publications of population census organizations.
• United Nations (1990), “World Population Monitoring 1989”, UNFPA.
• United Nations (1998), “World Population Assessment”, UNFPA; New York.
• United Nations (1996), “Added years of Life in Asia”, ESCAP; U.N., Thailand.
• Haupt, A., Kane, T. T., and Haub, C. (2011) PRB’s Population Handbook.

STAT- 401:         Statistical Inference-I

Course Objectives:

• To introduces students to the basic theory behind the development and assessment of statistical analysis.
• To understand the techniques in the areas of point and interval estimation, as well as hypothesis testing.
• To apply the statistical techniques to real data and draw conclusions.
• Learning Outcomes:

• Explain the notion of a parametric model and point estimation of the parameters of those models. Explain and apply approaches to include a measure of accuracy for estimation procedures and our confidence in them by examining the area of interval estimation.
• Asses the plausibility of pre-specified ideas about the parameters of a model by examining the area of hypothesis testing.
• Explain and apply the idea of non-parametric statistics, wherein estimation and analysis techniques are developed that are not heavily dependent on the specifications of an underlying parametric model.
• Understand the computational issues related to the implementation of various statistical inferential approaches.
• Course Contents:

Estimation of Parameters, Properties of Estimators: unbiasedness, consistency, sufficiency, efficiency, Invariance, completeness. Cramer-Rao inequality, Rao-Blackwell and Lehmann - Scheffe Theorems, Methods of Estimation: Moments, Maximum likelihood, least-squares, minimum Chi- square and Bayes’ method.

Pre-Requisite:   STAT-302 Recommended Books:

• Lindgren, B.W. (1998). “Statistical Theory”. Chapman and Hall, New York.
• Mood, A.M., Graybill, F.A. and Boss, D.C. (1997). “Introduction to the Theory of Statistics”. McGraw Hill, New York.
• Rao, C.R., (2009). “Linear Statistical Inference and its Applications”, John Wiley, New York.
• Rohatgi, V. K. (1984) Statistical Inference. Courier Dover Publications.
• Stuart, A. and Ord, J.K. (2009). Kendall’s’ “Advanced Theory of Statistics” Vol. II. Charles Griffin, London.

STAT- 402:         Statistical Inference-II

Course Objectives:

• To develop an advanced-level understanding and working knowledge of statistical inference.
• To provide an introduction to the rudiments of statistical inference for population parameters based on a general decision theoretic framework covering estimation and test of hypothesis.
• To introduce some nonparametric methods and their applications.

Learning Outcomes:

• A foundation for understanding probability-based statistical inference material presented in other courses.
• The understanding of the concepts of testing, size and power of a test.
• The understanding of and derivation of the properties of tests based on different criterion functions.

Course Contents:

Interval Estimation: Pivotal and other methods of finding confidence interval, confidence interval in large samples, shortest confidence interval, optimum confidence interval. Bayes’ Interval estimation

Tests of Hypotheses: Simple and composite hypotheses, critical regions. Neyman-Pearson Lemma, power functions, uniformly most powerful tests. Deriving tests of Hypothesis concerning parameters in normal, exponential, gamma and uniform distributions, Randomized Tests, Unbiased tests, Likelihood ratio tests and their asymptotic properties. Sequential Tests: SPRT and its properties, A.S.N. and O.C. functions.

Pre-Requisite:   STAT-401 Recommended Books:

• Hirai, A. S. (2012) Estimation of Parameters. Ilmi Kitab Khana Lahore.
• Lehman, E.L. (2008). “Testing Statistical Hypotheses”. Springler - Volga, New York.
• Lindgren, B.W. (1998). “Statistical Theory”. Chapman and Hall, New York.
• Rao, C.R., (2009). “Linear Statistical Inference and its Applications”, John Wiley, New York.
• Stuart, A and Ord, J.K. (2009). Kendall’s’ “Advanced Theory of Statistics” Vol. II. Charles Griffin, London.
• Welish, A. H. (2011) Aspects of Statistical Inference. Wiley.

STAT- 403:         Multivariate Analysis

Course Objectives:

• This course provides the fundamental knowledge of multivariate data and its applications in different fields of life.
• This course will introduce the students different multivariate techniques through real world problems.
• This course will develop the skill in students to estimate the parameters and drive inference in multivariate cases.

Learning Outcomes:

• Understand    the   basic   concepts   and   applications   of   multivariate techniques.
• Unable to decide which multivariate technique to be used for the given scenario.
• Analyze the multivariate data and interpret the results correctly.

Course Contents:

Introduction to multivariate data and its graphical representation. Euclidean and statistical distance. Review of matrix algebra, quadratic form, Eigen analysis, spectral decomposition. Descriptive statistics for multivariate data, multivariate normal distribution and its properties, Methods for testing multivariate normality, Inference about mean vector, Inference about covariance matrices, One-way multivariate analysis of variance (MANOVA), profile analysis

Pre-Requisite:   STAT-305 Recommended Books:

• Anderson, T.W. (2003). An Introduction to Multivariate Statistical Analysis, John Wiley & Sons, New York, USA.
• Johnson, R. A. and Wichern, D. W. (2007). Applied Multivariate Statistical Analysis, Prentice Hall, New York, USA.
• Manly, B.F.J. (2004). Multivariate Statistical Methods: A Primer, Chapman and Hall/CRC, New York, USA.
• Mardia, K. V., Kent, J. T. and Bibby, J. M. (1976). Multivariate Analysis, Academic Press, New York, USA.
• Rencher, A.C. and Christensen, W.F. (2012). Methods of Multivariate Analysis, John Wiley & Sons, New York, USA.

STAT- 402:         Statistical Inference-II

Interval Estimation: Pivotal and other methods of finding confidence interval, confidence interval in large samples, shortest confidence interval, optimum confidence interval. Bayes’ Interval estimation

Tests of Hypotheses: Simple and composite hypotheses, critical regions. Neyman-Pearson Lemma, power functions, uniformly most powerful tests. Deriving tests of Hypothesis concerning parameters in normal, exponential, gamma and uniform distributions, Randomized Tests, Unbiased tests, Likelihood ratio tests and their asymptotic properties. Sequential Tests: SPRT and its properties, A.S.N. and O.C. functions.

Pre-Requisite:   STAT-401 Recommended Books:

• Hogg,   R.V.   and   Craig,   A.T.   (1996).   “Introduction   to   Mathematical. Statistics”. Prentice Hall, New Jersey.
• Hirai, A. S. (2012) Estimation of Parameters. Ilmi Kitab Khana Lahore.
• Lehman, E.L. (2008). “Testing Statistical Hypotheses”. Springler - Volga, New York.
• Lindgren, B.W. (1998). “Statistical Theory”. Chapman and Hall, New York.
• Mood, A.M. Gray Bill, F.A. and Boss, D.C. (1997). “Introduction to the Theory of Statistics”. McGraw Hill, New York.
• Rao, C.R., (2009). “Linear Statistical Inference and its Applications”, John Wiley, New York.
• Stuart, A and Ord, J.K. (2009). Kendall’s’ “Advanced Theory of Statistics” Vol. II. Charles Griffin, London.
• Welish, A. H. (2011) Aspects of Statistical Inference. Wiley.
• Zacks, S. (1973), “Parametric Statistical Inference”, John Wiley, New York.

STAT- 422:        RESEARCH PROJECT / INTERNSHIP

Note: A separate and independent research project/internship will be assigned and completed by each student. At the end of the project/internship, it will be mandatory for each student to submit his/her project/research/internship report for evaluation.

ELECTIVE COURSES (BS)

STAT- 405:         Research Methodology

Course Objectives:

• To understand some basic concepts of research and its methodologies
• To identify appropriate research problems
• To select and define appropriate research problems and parameters
• To organize and conduct research in more appropriate manner
• Learning Outcomes:

• Understand general definition of research design
• Solve the problems in the fields of qualitative and quantitative research
• Plan and conduct research using an appropriate research design, keeping in view the ethical issues in the research
• Critically review and develop a complete research project
• Course Contents:

Definition of Research, Types of Research: Quantitave and Qualitative research. Plagiarism and ethics of research. Selection of Problem, Search of References, Formation of Hypothesis and Procedure for its Testing, Research Design, Planning of Experiments and surveys to Test Hypothesis Objectivity, Principals of Experimental Design, Steps in Experimentation, Designing Questionnaire, Collection of Data, Data Analysis, Functional/causal Relationship Between Variables, Levels of Significance, Interpretation of Results, Components of Scientific Reports and Various Methods of Data, Presentation, Preparation of Scientific Reports, Publication Procedures. Qualitative Research: content analysis.

NOTE:      Studying   and   reviewing   standard   survey   questionnaires   and preparation of a sample questionnaire and a scientific report.

Pre-Requisite:   STAT-304 Recommended Books:

• Saris, W.E. and Gallhoffer, I.N. (2014). Design, Evaluation, and Analysis of Questionnaires for Survey Research. 2nd edition. John Wiley & Sons, Inc, Hoboken, New Jersey.
• Panneerselvam, R. (2013). Research Methodology. Prentice Hall India.
• Singh, Y.K. (2011). Fundamental of Research Methodology and Statistics.New Age International limited.
• Daniel, P.S. and Sam, A.G. (2011). Research Methodology. Kalpaz Publications, Delhi.
• Salkind, N.J. (2010). Encyclopedia of Research Design. Sage Publications, Inc.
• Creswell, J.W. (2002). Research Design: Qualitative, Quantitative and Mixed Methods Approaches. Sage Publications.

STAT-406:          Operations Research

Course Objectives:

• To introduce students to the techniques of operations research.
• To provide students with basic skills and knowledge of operations research and its application in industry.
• To introduce students to practical application of operations research with emphasis on the industrial data.
• To effectively use relevant statistical software for data analysis.

Learning Outcomes:

• Identify and develop operations research models from the verbal description of the real system.
• Understand the mathematical tools that are needed to solve optimization problems.
• Apply operations research techniques to summarize the industrial data.
• Demonstrate the usage of statistical software for solving problem and analyzing the relevant data.

Course Contents:

History and definition of Operations Research (OR), Types of OR models, Introduction to linear programming, Formulation of LP model, Graphical solution of two variables, Standard Form, Simplex method, Duality theory; Sensitivity Analysis, Primal and dual form, Transportation Problem, Assignment problem. Network Analysis, PERT/CPM techniques, Queuing Models.

Recommended Books:

• Hillier, F.S. and Lieberman, G.J. (2014). Introduction to Operations Research. 10th edition. McGraw Hill.
• Bazarra, N.M., Jarvis J.J. and Sherali, H.D. (2010). Linear Programming and Network Flows. 4th edition. John Wiley & Sons.
• Taha, H.A. (2010). Operations Research. 9th edition, Pearsons.
• Gross, D., Shortle, J.F., Thompson J.M. and Harris, C.M. (2008). Fundamentals of Queueing Theory. 4th edition. John Wiley & Sons, Hoboken, NJ.
• Gupta, P.K. and Hira, D.S. (2008). Operations Research. 7th edition, S. Chand and Co., New Delhi.
• Bronson, R. and Naadmuthu, G. (1997). Operations Research – Schaums’ Outline Series. McGraw-Hill.

STAT- 407:         Stochastic Processes

Course Objectives:

• This course aims to provide an understanding of stochastic processes and the ability to analyze certain aspects of these processes.
• Accordingly, the course starts by reviewing probability theory, conditional probability, independence and certain properties of random variables, and continues by examining stationary processes.
• Furthermore, Markov chains in discrete and continuous time as well as Possion processes are investigated in detail.
• Learning Outcomes:

• Define probability models, concept and properties of random variables, random processes, Markov processes and Markov chains,
• Explain properties and functions of random processes with stochastic mathematical models, - formulate discrete and continuous time random processes, stationary random processes.
• Devise solutions with probability models for Poisson processes, discrete and continuous time Markov chains.
• Course Contents:

Introduction, Generating Functions, Laplace Transforms, Differential- Difference Equations, Introduction to Stochastic Processes. Types of stochastic process, stationary process. Random Walk, Expected Duration of the Game, Markov Chains, Transition Probabilities, Classification of States and Chains, Markov processes of discrete and continuous State Space, Poisson Process and its Generalization, Pure Birth and Death Processes, Random process, Weiner process, Introduction to Brownian motion.

Recommended Books:

• Durrett, R. (2001). Probability: Theory and examples, Cornel University, New York, USA.
• Freedman, D. (1999). Brownian Motion and Diffusion, Springer, New York, USA.
• Karlin, S.A. and Taylor, H.M. (2011). A first course in Stochastic Process, Academic Press, London, USA.
• Peter, W.J. and Smith,  P. (2010).    Stochastic Process: An Introduction, Chapman and Hall, New York, USA.
• Resnick,  S.  I.  (2002).  Adventure  in  Stochastic  Process,     Birkhauser Boosters, New York, USA.
• Ross, S.M. (2006). Stochastic Process, John Wiley & Sons, New York, USA.

STAT- 408:         Reliability Theory

Course Objectives:

• To learn to analyze complete and censored reliability data with and without covariates.
• To learn some key methods in reliability modeling.
• To learn the probability and statistical methods covered in the Reliability Analysis.
• To have the working knowledge to determine the reliability of a system and suggest approaches to enhancing system reliability.

Learning Outcomes:

• Analyze the interference between strength and stress, or life data for estimating reliability
• Apply the appropriate methodologies and tools for enhancing the inherent and actual reliability of components and systems, taking into consideration cost aspects.
• Specify life test plans for reliability validation.

Course Contents:

Basic concepts of reliability, Structural reliability, Life time distributions (Failure models): Hazard rate; Gamma, Weibull, Gumball, Log-Normal and Inverse Gaussian Distribution. Stochastic fatigue-rate models, Point and interval estimation, Fatigue-life model Testing reliability hypothesis, Monte-Carlo simulations, distribution-free and Bayes’ methods in reliability, System reliability; series and parallel systems, Failure models, (k-out-of-m) New-better-than used models. Inferences for these models, Accelerated life testing

Recommended Books:

• Jardine, A.K.S. and Tsang, A.H.C. (2013). Maintenance, Replacement and Reliability: Theory and Applications. 2nd edition. CRC Press.
• Elsayed, E.A. (2012). Reliability Engineering. 2nd edition. John Wiley & Sons.
• O’Connor, D.T. (2002). Practical Reliability Engineering. 4th edition. John Wiley & Sons.
• Gertsbakh, I.B. (1989). Statistical Reliability Theory. Marcel Decker. New York.
• Gertsbakh, I.B. (2009). Reliability Theory: with applications to preventive maintenance. Springer, India.

STAT- 409:         Time Series Analysis

Course Objectives:

• Learn basic analysis of time series data.
• Compute and interpret ACF/PACF and a sample spectrum.
• Derive the properties of ARIMA models and choose an appropriate ARIMA model for a given set of data and fit the model using an appropriate package
• Compute forecasts for a variety of linear methods and models.
• Learning Outcomes:

• Demonstrate understanding of the concepts of time series and their application to various fields of sciences.
• Apply ideas to real time series data and interpret outcomes of analyses and forecast.
• Use various advanced time series econometric methods, estimation methods and related econometric theories.
• Interpret time series models' estimates and analyze the results.
• Course Contents:

Time series analysis: concepts and components, Stochastic Process, Stationary Time-Series, Exponential smoothing techniques, auto-correlation and auto-covariance, estimation of auto-correlation function (ACF) and Partial autocorrelation function (PACF) and standard errors, Periodogram, spectral density functions, comparison with ACF, Linear stationary models: Auto Regressive Moving Average (ARMA) and mixed models, Non-stationary models, general ARIMA notation and models, minimum mean square forecasting. ARIMA Seasonal Models

Recommended Books:

• Enders, W. (2004). Applied time series econometrics. Hoboken: John Wiley and Sons.
• Box, G.E.P. and Jenkins, G.M., and Reinsel G. C. (2008) Time Series Analysis: Forecasting and Control, San Francisco.
• Chatfield C. (2003): The Analysis of Time Series: An Introduction, Taylor & Francis, NY, USA.
• Diggle, P.J. (1990), Time Series: A Bio statistical Introduction, Clarendon Press, Oxford.
• Jonathan D. C. and Kung-Sik C. (2008): Time Series Analysis with Applications in R, Springer, USA.
• Peter J. B and Richard A. D (2002): Introduction to Time Series and Forecasting, Second Edition, Springer, USA.

STAT- 411:         Robust Methods

Course Objectives:

• The objectives of this course is to provide an introduction to both basic and advanced analytical tools for robust models. This course also aims to promote a critical perspective on the use of statistical informations.
• Beginning with simple statistical methods, the course builds to more robust analytical techniques such as multivariate linear regression and estimators.
• Emphasis is placed on theoretical understanding of concepts as well as the application of key methodologies used in different research fields.

Learning Outcomes:

• Explain the importance, techniques and biases of estimators in context
• Explain the concept of outliers in regression model and other influential observations
• Construct and interpret various statistical hypothesis tests.

Course Contents:

Introduction to Robustness, Objective function, M-estimator of location, E- estimator, R-estimator and W-estimator, Redescending M-estimator’s The Breakdown point of Robust estimator Influence function. M-estimator for scale, Jackknife Resampling, Outliers and influential observations, Outliers in Regression analysis

Recommended Books:

• Hamper, T.R. Brochette, E. M., Rousseau, P.J. and Satchel, W.A. (1986). Robust Statistics: The approach Based on Influence functions, John Wiley & Sons, New York, USA.
• Hosmer, D.W. and Lemeshow, S. (2008). Applied Survival Analysis, John Wiley & Sons, New York, USA.
• Huber, P. J. and Ronchetti, E.M. (2009). Robust Statistics, John Wiley & Sons, New York, USA.
• Maronna, R.A.,  Martin, D.R. and  Yohai,  V.J. (2006).     Robust Statistics: Theory and Methods, John Wiley & Sons, New York, USA.
• Rousseau, P.J. and Leroy, A.M. (1987). Robust Regression and outlier detection, John Wiley & Sons, New York, USA.

STAT- 412:         Official Statistics

Course Objectives:

• To understand the official, demographic and social statistics.
• To understand the scope and organization of official statistics,
• To understand the planning and administration statistics.
• Learning Outcomes:

• The versatility to work effectively in a broad range of analytic, scientific, government, financial, technical and other positions.
• A broad overview of the fundamental issues underlying the organization of official statistics.
• To recognize the importance of statistical thinking.

Course Contents:

Introduction to official statistics, statistical systems and international standards, set up of national and provincial statistical organizations in Pakistan, its role in development of statistics, working and publications.

Sources of official statistics, National Database Registration Authority (NADRA) and its role, Economic Statistics producers, International classification and standards.

Use of Statistics in administration and planning concepts and evaluation of GDP, GNP, NNP, balance of Trade and payments. Measurements of income distribution, prices and price mechanisms. Deflation and Inflation of series, Industrial quantum index, National sample surveys and census conducted in Pakistan.

Note: Visit of major Statistical Organizations should be a part of the course. Alternatively, the department may invite experts from various statistical organizations.

Suggested Reports:

• Hansen M.H. (1980). Progress and Problems in Survey Methods and Theory. IIIustrated by the work of U.S. Bureau of the Census, U.S. Department of Commerce; A Monograph.
• NIPA (1962). Administrative uses of Statistics. NIPA Karachi.
• Statistical Institute for Asia and Pacific SIAP (1984). Training of Trainers in Statistical Operations and Procedures. Part-I, II UNDP, Tokyo.
• Statistics   Division   (1979).    Retrospect,    Perspective   and    Prospect. Islamabad.
• Statistics Division Activity Report (1988-89). Government of Pakistan, Islamabad.

*Various Publications of PBS, State Bank of Pakistan, Ministry of Finance, etc.

STAT- 413: Survival Analysis

Course Objectives:

• To introduce the basic concepts of survival analysis
• To describe and explain how survival analysis can be applied in different fields
• To learn the usage of appropriate statistical software for survival data analysis
• Learning Outcomes:

• Understand the basic concepts and ideas of survival analysis
• Derive properties and methods for standard survival time distributions
• Perform and interpret simple non-parametric survival analyses using software
• Apply and interpret semi-parametric regression models for survival data using software
• Course Contents:

Introduction to survival analysis with some important basic definition of statistical quantities, terminologies and notation of survival and hazard function, Censored Data and its three types, truncation ; importance and scope of the survival analysis. Describing the probability distributions of the survival and hazard functions. Basic layout of the survival problem both manually and computer based presentation of survival data. Computation of the descriptive measures for survival data both graphically and empirically. Estimation of the survival function, survival probabilities. Estimation of the survival functions from possibly censored samples by means of the Kaplan- Meier estimator, the Nelson-Aalen estimator and the kernel density estimator or the Ramlau-Hansen estimator and comparisons of k independent survival functions by means of the generalized log-rank test and related alternative approaches. The Proportional Hazards Model, the likelihood function, the Partial Likelihood Function, identification of Significant Covariates, estimation of the Survivorship Function with Covariates.Cox's semi-parametric models. Evaluation of the assumptions of Cox proportional hazard model. Introduction to estimation of Stratified Cox’s procedures for single and multiple variable adequacy Assessment of the Proportional Hazards Model.

Recommended Books:

• Collet, D. (2014). Modelling Survival Data in Medical Research. 3rd edition, CRC Press, Taylor and Francis Group. Fl, USA.
• Lee, E. T., and Wang, J. W (2013). Statistical Methods for Survival Data Analysis, 4th edition, John Wiley & Sons, New Jersey, USA.
• Kleinbaum, D.G. and Klein, M. (2012). Survival Analysis: A self learning text. 3rd edition. Springer, New York, NY, USA.
• Gjessing, H., Aalen, O. O. and Borgan, O. (2012). Survival and Event history analysis. Springer Series, New York, NY, USA.
• Machin, D., Cheung, Y. B. and Parmar, M. K. (2006). Survival Analysis: A practical approach. 2nd  edition,    John Wiley & Sons, Ltd. England, U.K.
• Klein, J. P., and Moeschberger, M. L. (2003). Survival Analysis: Techniques for Censored and Truncated data. 2nd edition, Springer series, New York, NY, USA.

STAT- 414:         Biostatistics

Course Objectives:

• To discuss and explain what biostatistics is and how it is used in Biological Sciences
• To recognize and give examples of different types of data arising in Biological Sciences
• To use statistical techniques to summarize the Biological data
• To apply statistical software to analyze and evaluate Biological data

Learning Outcomes:

• Understand the diverse applications of statistical tools in biological science.
• Demonstrate an understanding of the central concepts of modern statistical theory in Biological Sciences.
• Acquire the understanding of the appropriate usage of software for Biological sciences.
• Analyze and communicate the results of statistical analysis accurately and effectively.
• Course Contents:

Introduction to the basic concepts and terminology of Biostatistics, types of variables, populations, target populations and sampled population: Role of sampling in biostatistics, Sample size estimation. Contingency table analysis, Fisher’s exact test, 2x2 tables, Three way tables, rxc test for independence, Simpson’s paradox, Confounding, G-Test. Proportions, rates and ratios; incidence, prevalence, Odds Ratio, Relative Risk, Rate Ratio, Sensitivity and specificity. Distributional behavior of biological variables (Binomial, Poisson and Normal), Role of transformation for analysis of biological variables, Probit and Logit transformations and their analysis

Recommended Books:

• Sullivan, M.L. (2018). Essentials of Biostatistics in Public Health. 3rd edition. Jones and Bartlett Learning, Burlington, MA, USA.
• Antonisamy, B. Premkumar, P. and Christopher, S. (2017). Principles and Practice of Biostatistics. 1st edition. Elsevier, India.
• Alfassi Z. B., Boger, Z. and Ronen, Y. (2005): Statistical Treatment of Analytical Data. Blackwell Science, USA.
• Daniel, W.W. (2010). Biostatistics: A Foundation for the Health Sciences. 6th edition. John Wiley, New York. NY, USA.
• Dunn, G. and Everit, B. (1995). Clinical Biostatistics. Edward Arnold, London, UK.
• Zar, J. (2000). Biostatistical Analysis. 5th Edition. John Wiley & Sons, New York, NY, USA.

STAT- 415:         Data Mining

Introduction to databases including simple and relational databases, data warehouses, Review of classification methods from multivariate analysis; classification, decision trees: classification and regression trees. Clustering methods from both statistical and data mining viewpoints; vector quantization. Unsupervised learning from univariate and multivariate data; dimension reduction and feature selection. Supervised learning from moderate to high dimensional input spaces; introduction to artificial neural networks and extensions of regression models.

Recommended Books:

• Benson and Smith, S.J. (1997). “Data Warehousing, Data Mining’, and OLAP. McGraw-Hill.
• Bramer M (2007): Principles of Data Mining. Springer-Verlag London Limited UK.
• Breiman, L. Friedman, J.H. Olshen, R.A. and Stone, C.J. (1984). “Classification and Regression Trees” Wadsworth and Brooks/Cole.
• Han, J., Kamber, J. Pei, J., and Burlington, M. A. (2012) Data mining: concepts and techniques. Haryana, India.
• Han, J. and Camber, M. (2000). Data Mining; “Concepts and Techniques”. Morgan Gaufmann.
• Mitchell, T.M. (1997). “Machine Learning”. McGraw-Hill.
• Rao C. R., Wegman E. J. & Solka J. L (2005): Handbook of Statistics, Vol. 24: Data mining and data visualization. Elsevier B.V., North Holland.
• Ripley,   B.D.   (1996).   “Pattern   Recognition    and   Neural   Networks”. Cambridge University Press.
• Suh, S. C. (2012) Practical applications of data mining. Suh. Publisher
• Tan P., Steinbach M. & Kumar V. (2006): Introduction to Data Mining. Addison Wesley, New York.

STAT- 416:         Actuarial Statistics – I

Course Objectives:

• To develop understanding of the mathematical concepts and techniques that are used by actuaries to model stochastic processes of both assets and liabilities.
• To learn about various types of insurance and pension schemes.
• Learning Outcomes:

• Basic Mathematics involved in Actuarial Computations.
• Insurance, Types and Applications in Pakistan.
• Understanding the Life Contingencies and Actuarial Notations.
• Course Contents: Interest Rate Theory: Simple interest rate, Compound interest rate, Discount interest rate, Force of Interest, Real and Money Interest. Annuities: Description of annuities, Term annuity, Deferred annuity, Non-level annuities, Continuous annuities. Introduction to Actuarial Science, Role of Actuaries: Business, Finance, Stock Markets, Banks and other Financial Institutions. The role of Actuaries in Government Departments: SECP, State Bank, Employee Benefits Management. Insurance and Assurance, Types of Insurance: Life Insurance, Health Insurance, Motor Insurance, Businesses and Pension Fund. Islamic Mode of Insurance / Takaful. Life Insurance Contract: Define simple insurance contracts and devolve the formulae for mean and variance of the present values of the payments under these contracts, Whole life assurance, Term assurance, Pure endowment assurance, endowment assurance and critical ill- health assurance including assurances where the benefits are deferred also derive their mean and variances Define the symbols select and continuous equivalents.

Recommended books:

• Booth, P.M. et al. (1999). Modern Actuarial Theory and Practice, Chapman & Hall.
• Bowers, N.L. Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J. (1997). Actuarial Mathematics, Society of Actuaries, 2nd Edition.
• Broverman, S.A. (2015). Mathematics of Investment and Credit, 6th Edition, ACTEX Publications.
• Daniel, J.W. and Vaaler, L.J.F. (2007). Mathematical Interest Theory, Pearson, Prentice Hall.
• Dickson,   D.C.M.   Hardy,   M.R.   and   Waters,   H.R.   (2013).   Actuarial Mathematics for Life Contingent Risks, 2nd Edition.
• Gerber, H.U. (1997), Life Insurance Mathematics, Springer-Verlag, 3rd Edition.
• Johnson, A. (2016). Actuary Career (Special Edition): The Insider’s Guide to Finding a Job at an Amazing Firm, Acing the Interview & Getting Promoted.
• Miller, T. (2015). Achieving Your Pinnacle: A Career Guide for Actuaries.

STAT- 417:         Actuarial Statistics – II

Course Objectives:

• Developing an understanding of the mathematical concepts and techniques that are used to model and value cash flows contingent on survival, death and other uncertain events.
• Building mathematical foundations of life insurance and superannuation models.

Learning Outcomes:

• Understanding the Life Tables, Types and Computations.
• Understanding the Theories of Mortality, Analytical Laws and Projections.
• Develop and analyze the pension and benefit strategies that are equitable and meet the needs of diverse communities.

Course Contents:

Life Tables: Describe the life table functions, express life table probabilities in term of the actuarial related functions used both in assurances and annuities. Evaluation of assurances and annuities: derive the relations between assurance and annuities and their select and continuous equivalents. Net premiums and provisions: ultimate and select mortality; net premiums and net premium provisions, random future loss, , prospective and retrospective provisions, Derive Thiele’s equation, Death strain at risk, expected death strain, actual death strain, mortality benefits, Simple annuities and assurances involving two lives. Mortality: Theories of Mortality, analytical laws of mortality, techniques of projections of population mortality. Pension Theory: Structure and design of pension funds, Basic actuarial aspects of pension plans, Actuarial assumptions and actuarial cost methods, periodic gain and loss analyses, Relative merits of cost methods, sensitivity analysis.

Recommended books:

• Allen, et al. (2013). Retirement Plans: 401(k)s, IRAs, and Other Deferred Compensation Approaches, McGraw-Hill, 11th Edition.
• Benjamin, B. and Pollard, J.H. (2015). The Analysis of Mortality and other Actuarial Statistics, Society of Actuaries, 3rd Edition.
• Booth, P.M. et al. (1999). Modern Actuarial Theory and Practice, Chapman & Hall.
• Bowers, N.L. Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J. (1997). Actuarial Mathematics, Society of Actuaries, 2nd Edition.
• Gerber, H.U. (1997). Life Insurance Mathematics, Springer-Verlag, 3rd Edition.
• McGill, et al. (2010). Fundamentals of Private Pensions, Oxford University Press, 9th Edition.
• Yamamoto, D.H. (2015). Fundamentals of Retiree Group Benefits, ACTEX, 2nd Edition.

STAT- 418:         Mathematical Modeling and Simulation

Course Objectives:

• To understand the mathematical models using simulation
• To understand    the simulation approaches to problem solving, on a diverse variety of disciplines.
• To check the validity of models.
• Learning Outcomes:

• Recognize the connections between simulated and real data.
• Familiar with a variety of simulated examples where mathematical models helps accurately explain physical phenomena.
• Able to independently expand their mathematical or statistical expertise when needed, or for interest’s sake.
• Course Contents:

Monte Carlo methods: Different methods of generating random numbers, generation of random variables, acceptance and rejection techniques from various distributions. Comparison of algorithms to generate random variables, generating random variables from failure rates. Generation from multinomial distribution/Monte Carlo integration, Gibbs sampling and other resampling techniques, Variance reduction techniques: importance sampling for integration, control and antithetic variables.

Recommended Books:

• Daniel P. M, Maynard T. (2006). Mathematical Modeling and Computer Simulation, Thomson Brooks/Cole
• Fishman,    G.S.   (1996).    Monte   Carlo:    Concepts,   Algorithms,   and Applications. Springer.
• Ross, S.M. (2002). Simulation, 3rd Edition. Academic Press.
• Velten, K. (2009). Mathematical modeling and simulation. Wiley VCH, Germany.

STAT- 419:         Categorical Data Analysis

Course Objectives:

• To understand the basic concepts of categorical data analysis
• To recognize different types of categorical data and use appropriate methodology for categorical data
• To conduct statistical analysis using existing software and properly interpret the computer output.

Learning Outcomes:

• Implement basic categorical methods and combine them for the sampling estimation
• Obtain estimators, evaluate standard errors, construct confidence intervals and making statistical inference according to the categorical analysis techniques
• Apply the principles of lifelong learning to any new challenges arise with categorical data
• Demonstrate the knowledge to characterize, analyze and solve a wide range of problems related to the categorical data

Course Contents:

A brief history of categorical data analysis, Principles of likelihood-based inference, Sampling distributions for contingency tables, Measures of association for 2x2 tables, Testing independence in contingency tables, Exact inference for two-way tables, Inferences for three-way tables. Introduction to generalized linear models, Logistic regression, Model building, Alternative link functions for binary outcome, Diagnostics, Receiver Operating Characteristic (ROC) Curve Analysis. Exact methods and conditional logistic regression, Methods for analyzing matched case-control data, Multinomial response models for nominal data, Multinomial response models for ordinal data. Poisson regression model, Poisson regression for rates, Log linear models for contingency tables

Recommended Books:

• Agresti, A. (2012). Categorical Data Analysis. 3rd edition. John Wiley & Sons.
• Agresti, A. (2007). An Introduction to Categorical Data Analysis. 2nd edition. John Wiley & Sons.
• Hosmer D. W. and Lemeshow S. (2004). Applied Logistic Regression. John Wiley & Sons.
• Collett D. (2003). Modeling Binary Data. Champman and Hall/CRC.
• Lloyd C. J. (1999). Statistical Analysis of Categorical Data. John Wiley & Sons.
• Powers D. A. and Xie, Y. (2008). Statistical Methods for Categorical Data Analysis. 2nd edition. Emerald Group publishing

STAT- 422:         Bayesian Inference

Course Objectives:

• The aim of this course is to introduce the modern approach to Bayesian statistics,
• This   course   is   emphasizing    the   computational    aspects   and   the differences between the classical and Bayesian approaches.
• This course will help in formulating appropriate Bayesian models, including data and prior distributions.
• Learning Outcomes:

• Understanding basic techniques of Bayesian statistics for decision making
• Using different simulation techniques to handle complex posterior distribution
• Knowing the application of Bayesian statistics in different models
• Course Contents:

Introduction to Bayesian Inference, goals of Bayesian Inference, Conditional Probability, Conditional independence, Prior distribution and its different types, Posterior distribution, its mean, median (Bayes estimators under loss functions) and variances. Posterior Inference based on one parameter e.g. binomial, Poisson etc. Posterior inference based on normal distribution: Posterior predictive distributions, Bayesian Hypotheses Testing: Bayes factor; The highest density region; Introduction to Monte Carlo method, Discrete approximations.

Recommended Books:

• Albert, J. (2007). Bayesian Computation with R, 1st ed. Springer, New York, USA.
• Carlin, B. P. and Louis, T. A. (2008). Bayesian Methods for Data Analysis. Chapman & Hall/CRC Press, New York, USA.
• Congdon, P. (2006). Bayesian Statistical Modelling, John Wiley & Sons , New York, USA.
• Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2014). Bayesian Data Analysis. Chapman & Hall/CRC Press, New York, USA.
• Hoff, P.D. (2009). A First Course in Bayesian Statistical Methods, Springer, New York, USA.

STAT- 423:         Statistical Quality Control

Course Objectives:

• This course is designed to provide a conceptual and practical knowledge of techniques for quality control.
• This course is structured to monitor the process control via control charts.
• This course is designed to determine most appropriate sample size needed to accept or reject a lot of material.

Learning Outcomes:

• Design attribute and variable acceptance sampling plans for the industrial purpose.
• To construct various types of attribute and variable sampling plans using statistical software.
• Draw attribute and variable control charts to be implemented in different scenarios exist in industry.
• To construct various types of attribute and variable control charts to be implemented in different scenarios exist in industry.

Course Contents:

Concept of quality control and Quality assurance, Total Quality Management (TQM), Statistical Methods in Quality Improvement, Statistical Process Control (SPC). X-bar, R, S, Shewhart, CUSUM and moving average control charts. Six Sigma approach to control charts, Average Run Length (ARL); Standard deviation run length (SDRL). Process capability analysis: Process improvements using design of experiments. Acceptance sampling plans: Single, double, and multiple with their operatic characteristic curves. Introduction to ISO- 9000 and ISO-14000 series

Recommended Books:

• Juran, J.M. and Godfrey, A.B. (1998). Juan’s Quality Control Handbook. McGraw Hill, New York, USA.
• Montgomery, D.C. (2013). Introduction to Statistical Quality Control. McGraw Hill, New York, USA. Ryan, T.P. (2011). Statistical Methods for Quality Improvement. John Wiley & Sons, New York, USA.
• Schilling, E.G. and Neubauer, D.V. (2008). Acceptance Sampling in Quality Control. Chapman & Hall, New York, USA.
• Vardeman, S.B. and Jobe, J.M. (2016). Statistical Methods for Quality Assurance: Basics, Measurement, Control, Capability, and Improvement. Springer, New York, USA
NEWS & EVENTS Provisional Merit List for MPhil Mathematics Fall-2021

09 Sep 2021 list of provisionally admitted candidates for the admission in PhD Mathematics, Fall-2021

06 Aug 2021 