1. Each course is of 3 credits.
2. Course work shall be 24 credits.
3. Dissertation shall be 26 credits.
4. Total of 50 credits are to be completed for the award of M. Phil. degree.

Probability review, convergence of sequences, characteristic function, transformation of random variables, discrete and continuous probability models, Pearsonian system of distributions, Chebyclev-Hermetic polynomials, Gram-Charlier series, order statistics and their sampling characteristics, distribution of extreme values and noncentral chi, t and F distributions.

BOOKS RECOMMENDED

Stirzaker, D., Probability and Random Variables, Cambridge University Press, Cambridge. (1999).

Stuart, A., and Ord, K., Kendall’s Advanced Theory of Statistics Vol. I, Charles Griffin and Co., (1998).

Khan, M. K., Probability Theory with Applications, Maktaba Ilmi, Lahore, Pakistan (1994).

Rohatgi, S., Introduction to Probability Theory, McGraw Hill, (1976).

Feller, W., Introduction to Probability Theory and its Applications Vol. 1, John Wiley and sons, (1968).

Revision of simple random sampling, Construction of strata, Two way stratification, Deep stratification, Controlled sampling, Ratio estimators for population mean and population variance in the simple random sampling, Complex estimators in the simple random sampling, Chain estimators in the simple random sampling. Estimators in ranked set sampling, Estimators in stratified sampling, Multiphase sampling. No response, Imputation.

BOOKS RECOMMENDED

Cingi, H and Kadilar, C. Advances in Sampling Theory-ratio method of estimation, Bentham Science Publishers (2009).

Zakula, G. Elements of Sampling Theory and Methods, Prentice Hall (1999).

Cochran, W.G. Sampling Techniques, Jhon Wiley & Sons (1977).

Sukhatme, P.V., Sukhatme, D.V., Sukhatme, S. and Adok, C., Sampling Theory of Surveys with Application, Iowa State Uni. Press (1984).

Singh, S. Advanced Sampling Theory with Applications-How Michael selected Amy, Kluwar Academic Publishers (2003).

Sarndal, C. E, Swensson, B and Wretman, J., Model Assisted Survey Sampling, Springer-Verlag (1992).

Distribution of quadratic forms, general linear model: assumptions, estimation and testing. Testing for model assumptions. Ridge Regression and biased estimation. Simultaneous equations and multistage methods. Interval estimation and tests under the general linear fixed effects model with normally distributed errors, large sample theory for non-normal linear models. Two and higher way layouts, residual analysis. Effects of departures from the underlying assumptions. Robust alternatives to least squares.

BOOKS RECOMMENDED

Baltagi, B. H., Econometrics, 2nd Ed. Springer Verlag (1999).

Graybill, F. A., An Introduction to Linear Models: Theory and Applications, Duxbury, (1987).

Theil, H., Introduction to Econometrics, Prentice Hall, (1987).

Draper, N. R., and Smith, H., Applied Regression Analysis, John Wiley and sons, (1981).

Searle, S. R., Linear Models, John Wiley, New York (1971).

Sets, Indicator functions and classes of sets, measure space and probability space, measureable functions, integration theory and acception, Slutrky’s theorem, Dynkin’s theorem, Borel zero one law and kolmogrov’s zero one law. Levy’s inequality and Levy’s theorem, measure extension and Lebesgue-Stieltjes measure, comparison of Rieman and Lebesgue Integrals, product space and decomposition theorem.

BOOKS RECOMMENDED

Stuart, A., and Ord, K., Kendall’s Advanced Theory of Statistics, Vol. I, Charles Griffin and Co., (1998).

Friedett, B. & Gray, L., A modern Approach to Probability Theory, Birkhallsar, Boston. (1997).

Hole, P. G., Port and Stone, Introduction to Stochastic Processes, Houghton and Miffin, (1985).

Rohatgi, S., Introduction to Probability Theory and Mathematical Statistics, McGraw Hill, (1976).

Feller, W., Introduction to Probability Theory and its Applications Vol. 2, John Wiley and Sons, (1971).

Feller, W., Introduction to Probability Theory and its Applications Vol. 1, John Wiley and Sons, (1968).

Sufficiency and the minimal sufficient statistic, complete classes, Exponential families, Cramer-Rao lower bound and its extension, bias reduction by Jackknifing, ancilliary and Basu theorem, methods of estimation and their optimal properties, Bayes and minimax estimators, shrinkage estimation, sequential estimation.

BOOKS RECOMMENDED

Levy, P. S., and Lemeshow, S., Sampling of Populations Methods and Applications, 3rd Ed. John Wiley, New York (1999).

Lindgren, B. W., Statistical Theory, Chapman and Hall (1998).

Lehman, E. L., Theory of Point Estimation, John Wiley and sons (1987).

Rohatgi, V. K., Statistical Inference, John Wiley and Sons (1984).

Cox, D. R. and Hinkley, D. V., Theoretical Statistics, Chapman and Hall, (1978).

Neyman-Pearson theory of hypotheses testing, unbiased and invariant tests, likelihood ratio tests and their asymptotic properties, confidence estimations, Bayes confidence intervals, confidence regions, robustness and distribution- free procedures, sequentional tests.

BOOKS RECOMMENDED

Lahman, E. L., Testing Statistical Hypotheses, Springer Verlag, New York, (1997).

Rohatgi, V. K. Statistical Inference, John Wiley (1984).

Lindgren, B. W., Statistical Theory, McMillan Co. (1979).

Cox, D. R. and Hinkley, D. V., Theoretical Statistics, Chapman and Hall, (1978).

Probability proportional to size and with replacement (PPSWR) sampling methods, Use of more than one auxiliary variable in PPSWR, Multi-character survey, Estimation of correlation coefficient in PPSWR, Probability proportional to size and without replacement (PPSWOR) sampling, Horvitz and Thomson estimator, Model based estimation strategies, Calibration approach, Prediction approach, Poisson sampling, Cosmetic calibration, Dual frame surveys, Randomized response, Successive sampling, Cluster sampling, Adaptive sampling, Multistage sampling.

BOOKS RECOMMENDED

Cingi, H and Kadilar, C., Advances in Sampling Theory-ratio method of estimation, Bentham Science Publishers (2009).

Zakula, G., Elements of Sampling Theory and Methods, Prentice Hall (1999).

Cochran, W.G., Sampling Techniques, Jhon Wiley & Sons (1977).

Sukhatme, P.V., Sukhatme, D.V., Sukhatme, S. and Adok, C., Sampling Theory of Surveys with Application, Iowa State Uni. Press (1984).

Singh, S. Advanced Sampling Theory with Applications-How Michael selected Amy, Kluwar Academic Publishers (2003).

Sarndal, C. E, Swensson, B. and Wretman, J., Model Assisted Survey Sampling, Springer-Verlag (1992).

Basic designs: A review and analysis with unequal subclass numbers, 2n, 3n and mixed factorial experiments, Fractional replication and alias structure, Series of experiments in time and space, Analysis of Response surfaces/designs.

BOOKS RECOMMENDED

Montgomery, D. C., Design and Analysis of Experiments, John Wiley, New York (2000).

Boniface, D. R., Experimental Design and Statistical Methods, Chapman and Hall, (1995).

Garcia-Diaz, Alberto, Phillips, Don T, Jt. Auth, Principles of Experimental Design and Analysis, Chapman and Hall, (1995).

Harold, R. L., Analysis of Variance in Experimental Design, Springer Verlag, (1992).

Cochran, W. G., and Cox, G. M., Experimental Designs, John Wiley and Sons, (1992).

Maxwell, S. E. and Delancey, H. D., Designing Experiments and Analysis of Data, A Model comparison Perspective, Belmant and Wadeson, (1990).

Mead, R. The Design of Experiments – Statistical Principles for Practical Applications, Cambridge University Press, (1988).

Balanced and partially balanced incomplete block designs: construction, analysis, classification and existence. Competition designs and their analysis. Recent topics in the design of experiments.

BOOKS RECOMMENDED

Montgomery D. C., Design and Analysis of Experiments, John Wiley, New York (2001).

Cox, D. R, Reid, N., Jt. Auth. The Theory of the Design of Experiments, Chapman and Hall/CRC, Raton (2000).

Weber, Donald C., A First Course in the Design of Experiments; A linear Model Approach CRC Press, Boca Raton, (2000).

Boniface, D. R., Experiment Design and Statistical Methods, Chapman and Hall, (1995).

Harold, R. L., Analysis of Variance in Experimental Design, Springer Verlag, (1992).

Maxwell, S. E. and Delancey, H. D., Designing Experiments and Analysis of Data, A Model comparison Perspective, Belmant and Wadeson, (1990).

Mead, R. The Design of Experiments–Statistics Principles for Practical Applications, Cambridge University Press, (1988).

Models, Parameters and estimation using ML method, Transformations of parameters, inference and stable transformations. Computing Methods for Non-linear Modelling, Confidence intervals for parameters and functions. Applications of non-linear modelling.

BOOKS RECOMMENDED

Ross, G. J. S., Non-linear Estimation, Springer-Verlag, New York Inc., (1990).

Seber, G. A. F. and Wild, C.J., Non-linear Regression, New York John Wiley, (1989).

Kotz, S. and Johnson, N., Encyclopaedia of Statistical Sciences (Non-linear Models, Non-Linear Regression) N.Y. Wiley, (1985).

Ralkowsky, D.A., Non-Linear Regression Modelling, Dekker New York, (1984).

Bard Y., Non-linear Parametric Estimation, Academic Press, New York, (1974).

Fitting simple and multiple Logistic Regression Models using MLE, Non-iterative weighted Least Squares and discriminant functional analysis methods. Dichotomous, Polytomous and Continuous Independent Variables. Multivariate Case, Interaction and Confounding, Estimation of odds ratios in the presence of interaction. Model-building Strategies and Methods for Logistics Regression.

BOOKS RECOMMENDED

Lindsey, J. K., Applying Generalized Linear Models Springer-Verlag, New York Inc., (1997).

Kleinbaum, D. G., Logistic Regression: A self-learning text, Springer-Verlag, (1992).

McCullagh, P. and Nelder J. A., Generalized Linear Model 2nd Ed., London: Chapman and Hall, (1989).

Hosmer, D. W. and Hemeshow, Applied Logistic Regression, John Wiley, (1989).

Cox, D. R. and Oakes, D., Analysis of Survival Data, Chapman and Hall, (1984).

Utility theory; The utility of money; Rewards; Consequences; The loss functions; Development of the loss function from the utility theory; Certain standard loss functions for inference and predictive problems. Bayes estimators; Bayes predictors; Bayesian hypothesis testing under the different loss functions. Decision function; Multivariate loss function with Bayesian estimation. Risk; Types of risk. Choice of a sample size under posterior Bayes risk.

BOOKS RECOMMENDED

West, M. and Harrison, J. Bayesian Forecasting and Dynamic Models, 2nd Edition. Springer-Verlag, New York, (1997).

Robert, C. P., The Bayesian Choice: A Decision Theoretic Motivation, Springer-Verlag , New York, (1997).

Black-well and Grishick M.A., Theory of Games and Statistics Decisions, John Wiley and Sons Inc. New York, (1996).

O’ Hagan A, Kendall’s Advanced Theory of Statistics (V2B) Bayesian Inference, University Press: Cambridge, (1994).

Berger, J.O., Statistical Decision Theory & Bayesian Analysis, Springer-Verlag , New York, (1985).

General multivariate distributions, Multivariate normal distribution: Characterization and properties, linear forms and transformations, Related distributions: Wishart, Hotelling T2, Mahalanobis distance, etc. Behrens-Fisher problem, simultaneous confidence intervals and multivariate inference. Multivariate regression, sampling properties, hypothesis testing, correspondence analysis, uses in regression.

BOOKS RECOMMENDED

Richard, A. Johnson and Dean W. Wichem, Applied Multivariate Data Analysis 4th Edition. Prentice Hall International Inc. (1998).

Flury, B. A. First Course in Multivariate Statistics, Springer Verlag, New York (1997).

Manly, B. F. J., Multivariate Statistical Methods, 2nd Ed., Chapman and Hall, London (1994).

Morrison, D., Multivariate Statistical Methods, McGraw Hill, (1990).

Anderson, T. W., Introduction to Multivariate Statistical Analysis, John Wiley and Sons, (1984).

Mardia, K. V., Kent, J. T. and Bibby, J. M., Multivariate Analysis, Academic Press, (1979).

Multivariate analysis of variance: one-way and two way. Factor Analysis, factor and principal components, Analysis Canonical correlation analysis, Classification and Grouping Techniques: Discriminant and classification, clustering, distance methods and ordination.

BOOKS RECOMMENDED

Richard. A Johnson and Dean W. Wickern, Applied Multivariate Data Analysis 4th Edition. Prentice Hall International Inc. (1998).

Flury B., A first Course in Multivariate Statistics, Springer Verlag, New York (1997).

Manly, B. F. J., Multivariate Statistical Methods, A primer 2nd Ed., Chapman and Hall, London (1994).

Bian, S. Everitt and Grahm Dunn, Applied Multivariate Data Analysis. Edward. Arnold, Advision of Hodder and Stoughton Ltd. (1991).

Morrison, D., Multivariate Statistical Methods, McGraw Hill, (1990).

Anderson, T. W., Introduction to Multivariate Statistical Analysis, John Wiley and Sons, (1984).

Mardia, K. V., Kent, J. T. and Bibby, J. M., Multivariate analysis, Academic Press, (1979).

Smoothing and decomposition methods, regression and econometric methods, identification, estimation and diagnostic checking for linear models, Stationary and Non stationary ARIMA models. Forecasting using state space models and use of Kalman filter, Transfer function, intervention analysis and Bayesian forecasting. Box-Jenkins, Winner and Ross approaches to forecasting, Prediction VS Forecasting, multivariate Time Series Analysis, VAR Models, Co-integration Analysis.

BOOKS RECOMMENDED

Warner R.M., Spectral Analysis of Time Series data. Guilford Press New York, USA, (1998).

Chatfield C., The Analysis of Time Series-An introduction (5th Ed.) Chapman and Hall, London UK., (1996).

Enders, Walter, Applied Econometric Time Series, John Wiley and Sons, Inc. USA, (1995).

Box, G.E.P. and Jenkins G.M., Time-Series Analysis: Forecasting and Control 3rd Ed., Prentice Hall, Englewood Cliffs, N.J. USA, (1994).

Harvey, H.C., Time Series Models, Halstead Press, New York. USA, (1993).

Ostraom C.W., Time Series Analysis: Regression Techniques Sage Publications, Beverly Hills, C.A. USA, (1978).

Anderson, T., The Statistical Analysis of Time-Series, John Wiley and Sons. (1976).

Markov chains, discrete and continuous time Morkov chains, transition matrix and probabilities, spatial Poisson processes, compound and marked Poisson processes, renewal phenomenon, discrete renewal theory, branching processes and population growth, queuing systems, Brownian motion and martingales.

BOOKS RECOMMENDED

Grimmet, G. and Stirzaker, D., Probability and Random Processes, 3rd Ed. Oxford University Press (2001).

Koehler, U., and Soresen, M. Exponential Families of Stochastic Processes, Springer-Verlag, New York, (1997).

Suddhendu, B., Applied Stochastic Processes, A Bio statistical and Population Oriented Approach, New Age International Publishers Limited, Wiley Eastern Limited, UK: London, (1995).

Osaki, S. Stochastic System Reliability Modelling, world Scientific Publishing C. (1987).

Melhi, J., Stochastic Processor, John Wiley (1982).

Error analysis, Bazier and B Spline curves, Guassian Quadrature, Adaptive integrators, Multiple integration, Cubic splines, Boundary value problem, numerical solution of partial differential equations, approximation of function. Stochastic simulation: Generating uniform random variables, partial and general methods for non-uniform random variables, testing random numbers, building simulation models, variance reduction and statistical validation techniques.

BOOKS RECOMMENDED

Fishman, G. S., Principles of Discrete Event Simulation, John Wiley and Sons (1998).

Ross, S.M., A First Course in Simulation, Macmillan, New York (1990).

Froberg, C. E., Numerical Mathematics: Theory and Computer Applications, Benjamin Cummings, (1985).

Morgan B. J. T. , Elements of Simulation, Chapman and Hall, (1984).

Common non-parametric tests, Non-parametric analysis of variance, Non-parametric regression, robustness, breakdown and the influence cure, estimation using M, L and R Statistics, Contaminated distributions, Sampling-resampling Methods: Bootstrap and Jackknife. Confidence Intervals.

BOOKS RECOMMENDED

Conover, W. J., Practical Nonparametric Statistics, 3rd Ed., John Wiley and Sons. New York, (1999).

Maritz, J. S., Distribution Free Statistical Methods, Chapman and Hall, London, (1995).

Gibbons, J. D. and Chakrabortic, S., Nonparametric Statistical Inference, Marcel Dekker, New York (1992).

Rousseeuw, L., Robust Regression and Outlier Detection, John Wiley and Sons, (1987).

Huber, P., Robust Statistical Procedures, Society for Industrial and Applied Mathematics, (1987).

Hampel, J. W., Robust Statistics: The Approach Based on Influence function, (1986).

Randles, R. H. and Wolfe, D. A., Introduction to the Theory of Non-Parametric Statistics, John Wiley and sons, (1979).

State of Population: Stable and stationary population models, Theories of population growth, Population estimates and projections. Demographic effects of Population Growth. Economic, political and social implication. Consequences of a world population growth. Development of demographic profile in Pakistan. Pakistan’s place at global level, Recent demographic parameters, current and future demographic activities in Pakistan. Mathematical and Statistical Demography.

BOOKS RECOMMENDED

Hind, A., Demographic Methods, Arnold, (1998).

United Nations, Word Population Assessment, UNFPA; New York (1998).

Palmore, J. A. and Gardner, R.W., Measuring Mortality Increase, East West centre, Honolulu (1994).

Pollarad, A. H., Yusuf F., Pollard G. N. Demographic Technique. Pergamon Press, Oxford, Eng. (1983).

Natham K., Applied Mathematical Demography. Springer Verlag, New York. (1983).

Cox, P. R., Demography, Cambridge Univ. Press. (1978).

Statistical Applications, Mathematical aspects: identifiability, multimodality, negative mixing weights, general properties. Estimating mixing parameters: graphical methods, method of moments, maximum likelihood, Bayesian, minimum distance of distribution functions, minimum distance of transforms and numerical decomposition of mixtures.

BOOKS RECOMMENDED

Geoffrey, J. M., David, P., Finite mixture Models. Jhon Wiley & Sons (2001).

Bruce, L., Mixtures models: Theory, geometry and applications, institute of mathematical statistics (1995).

Titterington, D. M., Smith, A. F. H. and Markov, U. E. Statistical Analysis of Finite Mixture Distributions, John Wiley & Sons (1986).

Everitt, B. S. and Hand, D. J., Finite Mixture Distributions, Chapman & Hall, (1981).

Determining number of components of a mixture. Informal techniques, formal techniques for special cases and general formal techniques. Modality: structure and assessment. Sequential problems and procedures: unsupervised learning problems. Approximate solutions for: mixing parameters, component distribution parameters, mixing and component parameters and for dynamic linear models.

BOOKS RECOMMENDED

Geoffrey, J. M., David, P., Finite mixture Models. John Wiley & Sons (2001).

Bruce L., Mixtures models: Theory, geometry and applications, institute of mathematical statistics (1995).

Titterington, D. M., Smith, A. F. H. and U. E. Markov, Statistical Analysis of Finite Mixture Distributions, John Wiley & Sons (1986).

Everitt, B. S. and Hand, D. J., Finite Mixture Distributions, Chapman & Hall, (1981).

Introduction, Phases of experimentation, Historical development of clinical trials, Conduct of clinical trials, Analysis of clinical trials data, Cross over trials, Koch’s non-parametric approach, Interim analysis and sequential clinical trials.

This course will cover special topics of current research interest published in journals and will be taken care of by more than one teacher. Students will be expected to give presentations/seminars based on published articles and to write report.

Stochastic Processes and Financial time Series, Shock Persistence and impulse response analysis, Estimating Capital Asset Pricing Models (CAPM), Modeling of equity returns, trading day effects, and volatility estimations. In addition, recent advancements in financial time series including the unit root phenomenon, co-integration, Autoregressive Conditional Heteroscedasticity (ARCH) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH), stochastic volatility modeling, trend break analysis and nonlinearity will be covered Measure of Stock Market Integration.

BOOKS RECOMMENDED

Chatfield, C. (2004) The Analysis of Time Series, (5th Ed.) Chapman and Hall, New York.

Mills, T.C. (1993) The Econometric Modeling of Financial Time Series, Cambridge University Cambridge.

Campbell, J. Y., Lo, A. W. and Mackinlay, A. C. (1997) The Econometrics of Financial Markets. Princeton University Press.

James D. Hamilton (1994) “Time Series Analysis” Princeton University Press.

Population Growth Models, Development and Application of Lotka Integral Equation, Smoothing of age data by various methods, estimations of age at first marriage, child mortality, adult mortality, and fertility, construction of abridged life tables and decrement life tables, Lagrange estimates, and projections by application of straight line, logistic, Exponential, Gumpertz and Polynomial curves and by component method, Path Analysis for decomposition of effect of factors affecting and dependent variable.

BOOKS RECOMMENDED

Preston, S. H., Patrick, H. and Michel, G. (2001). Demography: Measuring and Modeling Population Process. Oxford: Blackwell Publishers.

Nathan K and Cawell, H (2004) Applied Mathematical Demography, Springer Verlag.

Shryok H., Seigal J. S. and Associates (1994). The methods and Materials of Demography (Condensed Ed.) New York, USA.

U. N. Feotal, Infant, and Early Childhood Mortality (1954). Vol. I & II, Series A, Population Studies No. XIII, Population Division, New York, U.S.A.

Coale A. and Demeny P. (1966). Regional Model Life Tables and Stable Populations. Princeton, N. J., Princeton University Press.

U. N. Manual on Methods of Estimating Population (1952). Manual III. Series A, Poulation Studies, Population Division, New York, U.S.A.

Lee-Jay Cho. (1973) “The Own-Children Approach to Fertility Estimation: An Elaboration,” Proceedings of International Population Conference, Vol. II, International Union For the Scientific Study of Population, Lige.

U. N. (1967) Methods of Estimating Basic Demographic Measures from Incomplete Data. Manual IV, Series A, Population Studies No. 42, Population Division, New York, U. S. A.

Introduction to statistical process control and its tools, Multivariate process monitoring through Hotelling T2charts. Chi-square chart, Generalized variance chart. Multivariate EWMA and CUSUM charts. Robustness and nonparametric approaches for process monitoring, Some bayesian structures for quality control, Covariates and process improvement, Process capability study, Introduction of six sigma, Designed experiment and process monitoring, Acceptance sampling and acceptance sampling plans. Advancements in techniques for quality improvement and quality assurance, Taghuchi’s methods for quality control, Evolutionary operation and process improvement, Introduction to statistical software’s for SPC.

Introduction to Randomized Response: Warner Model, the unrelated-question model, polychotomous population and multiattribute situations, Techniques for quantitative characteristics, Efficient estimation and protection of privacy, Miscellaneous topics on randomize response techniques: a bayesian approach, lying models, direct response and some allied methods for sensitive characters, Randomized Response in a finite population setting: sampling with unequal probabilities.

BOOKS RECOMMENDED

Chaudhuri, A. Randomized Response and Indirect Questioning Techniques in Surveys, Chapman & Hall (2011).

Chaudhuri, A. and Mukherjee, R. Randomized Response: Theory and Techniques, Marcel Dekker (1987).

Fox, J. A. and Tracy, P.E., Randomized Response: A Method for Sensitive Surveys, Sage Publications (1986).

Paul, M. Randomized Response Technique: getting in touch with touchy questions, COMAP Publisher (1981).

Wayne W. D., Collecting Sensitive Data by Randomized Response: an annotated bibliography, Georgia State University Business Press (1993).

Bayesian spatial statistics: prediction using plug-in estimates, Bayesian estimation and prediction for the Gaussian linear model, Trans-Gaussian model, Bayesian estimation and prediction for generalized linear Geostatistical model and case studies in respective fields. Hierarchical Bayesian models for spatial data analysis. Spatial-Temporal Models:
Spatio-temporal processes, stationarity of spatio-temporal processes. Separable versus non-separable covariance models, nested spatio-temporal covariance models. Space-time kriging based on Lagrange multiplier. Hierarchical Bayesian model for spatio-temporal prediction. Hierarchical Bayesian model for spatio-temporal prediction: including external drift.