MODEL SCHEME OF STUDIES FOR BS (4-YEAR) IN STATISTICS

Semester / Name of Subject Credits

Year

First

Introductory Statistics 3

Pakistan Studies 2

English-I (Functional English) 3

Calculus-I 3

General-I 3

General-II 3

Second

Introduction to Probability Distributions 3

Islamic Studies/Ethics 2

English-II 3

Calculus-II 3

General-III 3

General-IV 3

Third

Basic Statistical Inference 3

English-III 3

Introduction to Computer 3

General-V 3

General-VI 3

Fourth

Applied Statistics 3

Introduction to Regression Analysis & 3

Experimental Design

Communication Skills 3

Linear Algebra 3

General-VII 3

Fifth

Probability Distribution-1 3

Sampling Technique-I 4

Design & Analysis of Experiment-I 4

Regression Analysis 4

Statistical Packages 3

Sixth

Probability Distribution-II 3

Sampling Techniques-II 4

Design & Analysis of Experiment-II 4

Econometrics 4

Official Statistics 3

Seventh

Statistical Inference-1 3

Applied Multivariate Analysis 4

Time Series Analysis 3

Elective I 3

Elective-II 3

Eight

Statistical Inference-II 3

Population Studies 4

Research Project / Internship 3

Elective-III 3

Elective-IV 3

Total 132

Note: 4 credit hours courses must include Lab. /Practical.

Aims and Objectives

The major aims and objectives of the curriculum of Statistics are to adapt

the curriculum to meet the international standards.

1. To provide a sound footing of the subject matter of statistical theory

with applications, so that the students can pursue higher degrees and

research in the field of statistics.

2. To train the students in the use of statistical software and techniques of

data collection and analysis so that they can compete in the job

market.

3. To involve the students in research project so that they can be better

trained in the field of research.

4. To develop a solid foundation for the effective operational and strategic

decisions based on statistical theory and methodology in almost every

discipline.

* 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.

1. Business Administration (Entrepreneurship)

2. Human Resource Management

3. Environmental Sciences

4. Principles of Management & Marketing

5. Basic Financial Management

6. History of Human Civilization

7. Introduction to Biology

8. Foreign Language other than English

9. Introduction to Physics

10. Advanced Calculus

11. Introduction to Genetics

12. Introduction to Geography

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 - I

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, Meaures of

Dispersion: Their properties, usage, limitations and comparison. Moments,

Measures of Skewness and Kurtosis and Distribution shapes. Rates and

ratios, Standardized scores

Recommended Books

1. A basic course in statistics / G.M. Clarke, D. Cooke. Edition: 5th

ed. Publisher: London : John Wiley, 2004

2. Chaudhry, S.M.and Kamal, S. (2008), “Introduction to Statistical

Theory” Parts I & II, 8th ed, Ilmi Kitab Khana, Lahore, Pakistan.

3. Mann, P. S. (2010) Introductory Statistics. Wiley.

4. Mclave, J.T.,Benson, P.G. and Snitch, T. (2005) “Statistics for

Business & Economics” 9th ed. Prentice Hall, New Jersey.

5. Schaum's outline of theory and problems of beginning statistics /

Larry J. Stephens. Edition: 2nd ed. Publisher: New York : McGraw-

Hill, 2006

6. Spiegel, M.R., Schiller, J.L. and Sirinivasan, R.L. (2000)

“Probability and Statistics”, 2nd ed. Schaums Outlines Series.

McGraw Hill. NY.

7. Sullivan, M., Fundamentals of statistics, III. Edition: 3rd ed.

Publisher: Boston: Prentice Hall, 2011.

8. Walpole, R.E., Myers, R.H and Myers, S.L. (1998), “Probability and

Statistics for Engineers and Scientist” 6th edition, Prentice Hall, NY.

9. Weiss, N.A.(1997), “Introductory Statistics” 4th ed. Addison-Wesley

Pub. Company, Inc.

10.

STAT- 102: Introduction to Probability & Probability

Distributions

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:

1. Cacoullos, T., Exercises in probability, Publisher: New York: Springer-

Verlag, 2009

2. Chaudhry, S.M.and Kamal, S. (2008), “Introduction to Statistical

Theory” Parts I & II, 8th ed, Ilmi Kitab Khana, Lahore, Pakistan.

3. Mann, P. S. (2010) Introductory Statistics. Wiley.

4. Clark, G.M. and Cooke, D. (1998), “A Basic Course in Statistics” 4th ed,

Arnold, London.

5. Mclave, J.T., Benson, P.G. and Snitch, T. (2005) “Statistics for

Business & Economics” 9th Edition. Prentice Hall, New Jersey.

6. Santos.D., Probability: an introduction, Publisher: Sudbury, Mass.:

Jones and Bartlett Publishers, c2011.

7. Spiegel, M.R., Schiller, J.L. and Sirinivasan, R.L. (2000) “Probability

and Statistics”, 2nd ed. Schaums Outlines Series. McGraw Hill. NY.

8. Walpole, R.E., Myers, R.H and Myers, S.L. (2007), “Probability and

Statistics for Engineers and Scientist” 7th edition, Prentice Hall, NY.

9. Weiss, N.A. (1997), “Introductory Statistics” 4th ed. Addison-Wesley

Pub. Company, Inc.

STAT- 202: Basic Statistical Inference

Sampling distribution: concepts and properties, Central limit theorem.

Estimation: Point Estimation. Desirable Properties of a Good Estimator,

Interval Estimation, Interval Estimation of population mean. Large and

small sample confidence intervals for Population Mean

Nature of Hypothesis Testing and Types of errors, Hypothesis Testing for

Population Mean and variance

Inferences for Two Population Means, Large-sample inferences for Two

Populations using Independent Samples, Inferences for the Mean of Two

Normal Populations using Independent Samples (variances are assumed

Equal/Not Equal). Inference for Two Populations Mean using Paired

Samples

Inferences for Population Proportions, Confidence Intervals and hypothesis

testing for Population Proportion, Inferences for Two Populations

Proportions using Independent Samples, Estimation of sample size Pre-Requisite- STAT-102

Recommended Books:

1. Chaudhry, S.M. and Kamal, S. (2008), “Introduction to Statistical

Theory” Part I, II, 8th ed, Ilmi Kitab Khana, Lahore, Pakistan.

2. Clark, G.M. and Cooke, D. (1998), “A Basic Course in Statistics” 4th

ed, Arnold, London.

3. Mclave, J.T., Benson P.G. and Snitch, T. (2005) “Statistics for

Business & Economics” 9th Prentice Hall New Jersey.

4. Spiegel, M.R., Schiller, J.L. and Sirinivasan, R.L. (2000) “Probability

and Statistics”, 2nd ed. Schaums Outlines Series. McGraw-Hill. NY.

5. Walpole, R.E., Myers, R.H. and Myers, S.L. (2007), “Probability and

Statistics for Engineers and Scientist” 7th edition, Prentice Hall, NY.

6. Weiss, N.A. (1997), “Introductory Statistics” 4th ed. Addison-Wesley

Pub. Company, Inc.

STAT- 203: Introduction to Regression Analysis and

Experimental Design

Concepts of Regression and Correlation, Simple Linear regression,

multiple linear regression, Inference regarding regression parameters,

linear correlation: simple, partial and multiple correlation, Inference

regarding correlation coefficient, Coefficient of determination

One-Way and Two-Way Analysis of Variance

Design of Experiments, Basic Principles of Design of Experiments,

Description, Layout and Analysis of Completely Randomized Design,

Randomized Complete Block Design and Latin Square Design, Multiple

Comparisons (LSD and Duncan’s test)

Pre-Requisite: STAT-101

Recommended Books:

1. Chaudhry, S.M., and Kamal, S., (2009), “Introduction to Statistical

Theory” Part I, II, 8th ed, Ilmi Kitab Khana, Lahore, Pakistan.

2. Clark, G. M. and Kempston, R. E. (1997), “Introduction to the Design

& Analysis of Experiment” Arnold London.

3. Walpole, P.E., Myers R.H., Myers S.L. (2007), “Probability and

Statistics for Engineers and Scientists”, 7th ed. Prentice Hall.

4. Weiss, N.A, (1997), “Introductory Statistics” 4th ed. Addison-Wesley

Pub. Company, Inc.

STAT- 201: Applied Statistics

Sampling: Sample versus population, Sampling, advantages of sampling,

statistic and parameter. Probability sampling techniques: Simple Random

sampling, Stratified random sampling, Systematic random sampling,

Cluster Sampling. Non-probability sampling techniques: Quota sampling,

purposive sampling, Snowball sampling. Census and survey problem,

framing of questionnaire, Sampling and Non-Sampling Errors

Index numbers: construction and uses of index numbers, un-weighted

index numbers (simple aggregative index, average of relative price index

numbers), weighted index numbers (Laspayers, Paaches and Fishers ideal

index numbers), Consumer price index (CPI) and Sensitive Price Indicators

Time Series Analysis: Components of time series and their decomposition.

Vital Statistics : 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.)

Pre-Requisite: STAT-101

Recommended Books:

1. Chaudhry, S.M. and S. Kamal, (2009), “Introduction to Statistical

Theory” Part I, II, 8th Ed, IImi Kitab Khana, Lahore, Pakistan.

2. Clark, G.M. and Cooke, D. (1998), “A Basic Course in Statistics” 4th

ed, Arnold, London.

3. Cochran, W.G. (1977) “Sampling Techniques”.3rd Ed.

4. Mclave, J.T. Benson, P.G. and Snitch, T. (2005) “Statistics for

Business & Economics” 9th Edition, Prentice Hall, New Jersey.

5. Pollard, A.H. Yousuf, F. and Pollard G.M. (1982), “Demographic

Techniques”, Pergamon Press, Sydney.

6. Walpole, P.E. Myers, R.H., Myers S.L. (1998), “Probability and

Statistics for Engineers and Scientists”, Prentice Hall.

STAT- 204: Statistical Packages

Introduction to Minitab, data manipulation in Minitab, graphical

representation in Minitab, Qualitative and Quantitative data presentation

and analyzing data in Minitab, Programming in Minitab

Introduction of SPSS, data manipulation in SPSS, simple arithmetic in

SPSS, SPSS function related to probability distributions, SPSS modules,

simple graphing in SPSS

Analysis using SPSS syntax programming

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

the Software.

Pre-Requisite: STAT-202

Recommended Books:

1. Colin D. Gray and Paul R. Kinnear, IBM SPSS statistics 19 made

simple. Publisher: New York: Psychology Press, 2012.

2. Kerr A. W., Hall, H. K., and Kozub, S. A. (2002) Doing Statistics with

SPSS. Sage Publications.

3. SPSS (2010) SPSS Statistics 19 Core System User’s Guide.

4. Marques de Sá, Joaquim P.( 2003) Applied Statistics using SPSS,

STATISTICA and MATLAB

5. Norusis, Marija (2006) SPSS 14.0 Guide to Data Analysis, Prentice

Hall, New Jersey.

6. Ryan, Barbara F.; Joiner, Brian L. and Cryer, Jonathan D.(2005)

MINITAB Handbook, 5th Edition, Duxbury Press, California.

7. Susan A. Nolan and Thomas E. Heinzen. Study Guide & SPSS

Manual to accompany statistics for the behavioral sciences Edition:

2nd ed. Publisher: New York : Worth Publishers, 2012

STAT- 301: Probability Distributions-I

Distribution function, Probability mass function and probability density

function. Joint and conditional distributions for two and more random

variables, Marginal and conditional distributions, stochastic independence,

Baye’s theorem, Mathematical expectation and its properties Conditional

expectation, variance and moments, Probability generating function,

Moment generating and characteristic functions and their properties,

Relation between moments and cummulants, Probability distributions:

Bernoulli, Binomial, Hypergeometric, Poisson, Negative binomial, Geometric, Multinomial distribution. Normal approximation to binomial &

Poisson distribution, Normal distribution with moments and cummulants

Pre-Requisite: STAT-102

Recommended Books

1. Fridett, B. & Gray, L. (1997). “A Modern Approach to Probability

Theory” Birkhallser, Boston.

2. Freund, J. E. (1997). “Mathematical Statistics”, Prentice Hall, New

Jersey 6th edition.

3. Haq, M. (1984). Foundation of Probability and Statistics, Tahir sons,

Urdu Bazar, Karachi.

4. Hirai, A.S. (2002), “A Course in Mathematical Statistics”, Ilmi Kutab

Khana, Lahore.

5. Hogg, R.M. and Craig, A.T. (1995), “Introduction to Mathematical

Statistics”. Prentice Hall, Engle wood Cliffs, New Jersey.

6. Khan, M. K., (1996). “Probability with Applications”, Maktiba Ilmi,

Lahore.

7. Mood, A.M, Graybill, F.A. and Boes, D.C. (1997), “Introduction to the

Theory of Statistics”, McGraw Hill, New York.

10. Norman L. Johnson , Samuel Kotz , N. Balakrishnan (1994).

Continuous Univariate Distributions, Vol. 1 (Wiley Series in

Probability and Statistics), Wiley-Interscience: New York.

11. Samuel Kotz , N. Balakrishnan, Norman L. Johnson (2000).

Continuous Multivariate Distributions, Volume 1, Models and

Applications, 2nd Edition, Wiley-Interscience: New York.

12. Sheldon Ross (2009). First Course in Probability, (8th Edition),

Pearson

Stirzaker, D. (1999). “Probability and Random Variables”. Cambridge

University Press, Cambridge.

13. Stuart, A. and Ord, J .K. Kendall’s’ (1998), “Advanced Theory of

Statistics”, Vol. I, Charles Griffin, London.

STAT- 303: Sampling Techniques-I

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, Systematic sampling, Ratio and regression

estimates in simple and stratified random sampling

Pre-Requisite: STAT-201

Recommended Books:

1. Brewer, K. R. & Hanif, M. (1983). Sampling with Unequal Probabilities,

Lecture Notes in Statistics Series, No. 15, Springer Verlag.

2. Bethelem, J. (2009) Applied Survey Methods: A Statistical

Perspective. Willey.

3. Chambers, R. L., and Skimmer, C. J. (2003) Analysis of Survey

Data. Wiley.

4. Chaudhary, A., and Stemger, H. (2005), Survey sampling theory and

methods. Chapman & Hall.

5. Cochran, W.G. (1977), “Sampling Techniques”, 3rd ed, John Wiley

and Sons, New York.

6. Ferguson, T.S. (1996), “A Course in large Sample theory, Chapman

& Hall, London.

7. Kish, L. (1992). “Survey Sampling”, John Wiley, New York.

8. Paduri S. R. S. Rao (2000) Sampling Methodologies with

Applications, Chapman & Hall

9. Raj, D. (1971) “Design of Sample Survey”. McGraw Hill, New York.

10. Raj, D. & Chandhok, P. (1998), “Sample Survey Theory”. Narosa

Publishing House, New Delhi.

11. Singh, R. and Singh N, (1996), “Elements of Survey Sampling”,

Kulwar Academic Publisher, Dodrecht.

12. Sukhatme, P.V, Sukhatme, B., Sukhatme, S., and Asok, A. (1985),

“Sampling Theory of Survey with Application”. Iowa State University

Press

STAT- 307: Regression Analysis

General linear model and its assumptions, Least squares estimators,

Maximum Likelihood Estimator, tests of significance for regression model

and regression parameters. Confidence intervals for regression

parameters, Test of linearity of regression, Use of extraneous information in linear regression model. Residual analysis, Detection and study of

outliers, Polynomial regression, orthogonal polynomial, orthogonal

regression analysis, Specification of models

Pre-Requisite: STAT-203

Recommended Books:

1. Baltagi, B. H. (1999). “Econometrics”, 2nd Edition, Springer Varlog.

2. Johnston, J. and Di. Nardo, J., (1997). “Econometric Method”, 4th

Edition, McGraw-Hill, New York.

3. Maddela, G.S. (1977). “Econometrics”, McGraw Hill. New York.

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

5. Yan, X. and Zu, X. G. (2009) Linear Regression Analysis: Theory &

Computing. World Scientific Publications.

6. Wonnacott, T.H. and Wonnacott R.J. (1998). “Econometrics”, John

Wiley, New -York.

STAT- 305: Design and Analysis of Experiments-I

Principles of Design of Experiments, Analysis of variance and its

assumptions, Cochran theorem, Fixed, random and mixed effect models,

Completely Randomized, Randomized Complete Block, Latin square,

Graeco-Latin square and cross-over designs, Missing observations,

Relative efficiency of designs, Estimation of mean squares and their

expectations, Multiple Comparisons tests

Analysis of covariance in CR, RCB designs, Estimation of missing values

in analysis of covariance.

Effect of violation of assumptions and transformations

Pre-Requisite: STAT-203

Recommended Books:

1. Boniface, D.R. (1995). “Experiment Design & Statistical Methods”,

Chapman & Hall.

2. Cochran, W.G. and Cox, G.M. (1992). “Experimental Design”, John

Wiley, New York. 3. Clarke, G.M. (1994). “Statistics & Experimental Design”. Edward

Arnold.

4. Clarke, G.M., and Kempton, R.E. (1997), “Introduction to the Design

& Analysis of Experiments”, Edward Arnold.

5. Das, M.N.and Geri, N.C, (1986). “Design and Analysis of

Experiments”, John Wiley, New York.

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

Agricultural Research”, 2nd Edition, John Wiley, New York.

7. Harold, R. L (1992). “Analysis of Variance in Experimental Design” .

Springer Verlage

8. Hicks, C.R. (1982). “Fundamental Concepts in Design and Analysis

of Experiments” Saunders

9. Hunter, B. and Hunter, W. G. (2005) Statistics for Experimenters:

Design, Innovation and Discovery. Wiley.

10. Maxwell, S.E. and Delaney, H.D. (1990). “Designing Experiments

and Analysis of Data”. A model comparison perspective. Belment

and Wadeson.

11. Mead, R. (1988). “The Design of Experiments”. Cambridge

University Press, Cambridge.

12. Montgomery, D. C., Design and analysis of experiments, Edition: 7th

ed. Publisher: New Jersey : John Wiley, 2009

13. Myers, R.H. and Montgomery, D.C. (1995). “Response Surface

Methodology; Process & Product Optimization Using Design”, John

Wiley.

14. Steel, Robert, G. D., Terrie James H., and Dickey David A. (1997).

“Principles and Procedures of Statistics: A Biometrical Approach” 3rd

Edition, McGraw-Hill, New York.

STAT- 310: 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.

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:

1. Conover, W.J. (1999), Practical Nonparametric Statistics, 3rd Edition,

John Wiley and Sons, New York

2. Gibbons, J.D. and Chakraborti, S. (1992), Nonparametric Statistical

Inference, Marcel Decker, New York.

3. Lehman, E.L. (1973), Nonparametric Statistical Methods, based on

Ranks, Holden-Day San Francesco

4. Maritz, J.S. (1995). Distribution-Free Statistical Methods, Chapman &

Hall London

5. Sprint, P. (2007). Applied Nonparametric Statistical Methods, 4th

edition, Chapman & Hall London

STAT- 302: Probability and Probability Distributions-II

Uniform, Lognormal, Exponential, Gamma, Laplace, Rayleigh, Weibell with

moments and cummulants; Distributions of functions of random variables:

Chi-square, t and F distributions, their derivations and properties. Central

limit and Chebyshev's theorems and other inequalities, Weak and Strong

Laws of large numbers and their applications, Order statistics, Distributions

of rth and sth order statistics, Bivariate Normal distribution.

Pre-Requisite: STAT-301

Recommended Books:

1. Dekking, F. M., Kraaikamp, C., and Lopuhaae, H. P., and Meester,

L. E. (2005) A Modern Introduction to Probability and Statistics.

Springer.

2. Fridett, B. & Gray, L. (1997). “A Modern Approach to Probability

Theory” Birkhallser, Boston.

3. Freund, J. E. (1997). “Mathematical Statistics”, Prentice Hall, New

Jersey.

4. Haq, M. (1984). “Foundation of Probability and Statistics”, Tahir sons,

Urdu Bazar, Karachi.

5. Hirai, A.S. (1998), “A Course in Mathematical Statistics”, Ilmi Kutab

Khana, Lahore.

6. Hogg, R.M. and Craig, A.T. (1995), “Introduction to Mathematical

Statistics”. Prentice Hall, Engle wood Cliffs, New Jersey.

----------------------- Page 25-----------------------

7. Khan, M. K., (1996). “Probability with Applications”, Maktiba Ilmi,

Lahore.

8. Mood, A.M, Graybill, F.A. and Boss, D.C. (1997), “Introduction to the

Theory of Statistics”, McGraw-Hill, New York.

9. Stirzaker, D. (1999). “Probability and Random Variables”. Cambridge

University Press, Cambridge.

10. Stuart, A. and Ord, J .K. Kendall’s (1998), “Advanced Theory of

Statistics”, Vol. I, Charles Griffin, London.

STAT- 304: Sampling Techniques-II

Cluster Sampling, Sub sampling, PPS-Sampling, Double Sampling,

Multistage and Multiphase sampling, Thomson Hurwitz estimator,

Comparison of different sample designs; non-response, their sources and

bias, Randomized response, Critical study of National sample surveys

conducted in Pakistan: Census of Agriculture Pakistan, Pakistan

Demographic Survey (PDS) and National Population and Housing Census

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:

1. Brewer, K. R. & Hanif, M. (1983). Sampling with Unequal

Probabilities. Lecture Notes in Statistics Series, No. 15, Springer

Verlag.

2. Bethelem, J. (2009) Applied Survey Methods: A Statistical

Perspective. Wiley.

3. Chambers, R. L., and Skimmer, C. J. (2003) Analysis of Survey

Data. Wiley.

4. Chaudhary, A., and Stemger, H. (2005), Survey sampling theory and

methods. Chapman & Hall.

5. Cochran, W.G. (1977), “Sampling Techniques”, John Wiley and

Sons, 3rd ed, New York.

6. Des Raj, (1971), Design of Sample Survey. McGraw-Hill, New York.

7. Des Raj & Chandhok, P. (1998), “Sample Survey Theory”. Narosa

Publishing House, New Delhi. 8. Ferguson, T.S. (1996), “A Course in Large Sample Theory” ,

Chapman & Hall, London.

9. Hansen, M. H., Hurwitz, W. N. & Madow, W.G. (1952).

10. Kish, L. (1992), “Survey Sampling”, John Wiley, New York.

11. Singh, R. and Singh N, (1996), “Elements of Survey Sampling”,

Kulwar, Dodrecht.

12. Sukhatme, P.V, Sukhatme, B., Sukhatme, S., and Asok, A. (1985),

“Sampling Theory of Survey with Application”. Iowa State University

Press.

13. Sukhatme, P.V, Sukhatme, B., Sukhatme, S., and Asok, A. (1985),

“Sampling Theory of Survey with Application”. Iowa State University

Press.

14. Various publications of Pakistan Bureau of Statistics (PBS).

15. Hansen, M. H., Hurwitz, W. N., and Madow, W. G. (1993) Sampling

Survey Methods and Theory, Vol. 1 and II, Wiley.

STAT- 308: Econometrics

Introduction to econometrics, Problems of autocorrelation, multicollinearity,

heteroscedasticity and their solution; Ridge regression, Lagged variables,

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.

Pre-Requisite: STAT-307

Recommended Books:

1. Baltagi, B. H. (1999). “Econometrics”, 2nd Edition, Springer Varlog.

2. Draper, N.R. and Smith, H. (2004). “Applied Regression Analysis” ,

John Wiley, New York.

3. Gujrati, D. (2004). “Basic Econometrics”, John Wiley, New York.

4. Guttmann, I. (1980); “Linear Models: An Introduction”, John Wiley,

New York.

5. Johnston, J. and Di. Nardo, J., (1997). “Econometric Method”, 4th

Edition, McGraw Hill, New York.

6. Koutsoyiannis, A. (1980), “Theory of Econometrics”, Macmillan.

7. Montgomery, D.C., and Peck E.A. (1992). “Introduction to Linear

Regression Analysis” , 2nd Edition. John Wiley and sons Inc. New

York

8. Wonnacot, T.H. and Wonnacot R.J. (1998). “Econometrics”, John

Wiley, New York

STAT- 306: Design and Analysis of Experiments-II

k k

Factorial Experiments: 2 , 3 series and mixed level factorial experiments

and their analyses.

Confounding in factorial experiments, Complete and partial confounding,

Confounding in Fractional replications. Split-plot, split-split plot, strip plot

and nested designs. Missing observations in Split plot design. Response

surface designs.

Incomplete block designs: BIBD - Lattice designs, lattice square and

Youden squares, PBIBD with recovery of intra-block information.

Pre-Requisite: STAT-305

Recommended Books:

1. Boniface, D.R. (1995). Experimental Design & Statistical Methods ,

Chapman & Hall.

2. Clarke, G.M. (1994). “Statistics & Experimental Design”. Edward

Arnold.

3. Clarke, G.M., and Kempton, R.E. (1997), “Introduction to the Design

& Analysis of Experiments”, Edward Arnold.

4. Das, M.N.and Giri, N.C, (1986). “Design and Analysis of

Experiments”, John Wiley, New York.

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

Agricultural Research”, 2nd Edition, John Wiley, New York.

6. Giesbrecht, F. G., Gompertz, M. L. (2004) Planning, Construction,

and Statistical Analysis of Comparative Experiments. Wiley.

7. Harold, R. L (1992). “Analysis of Variance in Experimental Design” .

Springer Verlag:

8. Hicks, C.R. (1982). “Fundamental Concepts in Design and Analysis

of Experiments”; Saunders

9. Maxwell, S.E. and Delaney, H.D. (1990). Designing Experiments and

Analysis of Data. A Model Comparison Perspective . Belmont and

Wadeson.

10. Mead, R., Gilmour, S., and Mead, A. (1990) Statistical Principles for

the design of experiments: Applications to real experiments.

Cambridge University Press, Cambridge.

11. Montgomery, D.C. (2000). “Design and Analysis of Experiments”,

John Wiley, New York

12. Myers, R.H. and Montgomery, D.C. (1995). “Response Surface

Methodology; Process & Product Optimization Using Design”, John

Wiley

13. Steel, G. D., Terrie, and Dickey A. (1997). “Principles and Procedures

of Statistics: A Biometrical Approach ” 3rd Edition, McGraw-Hill, New

York

STAT- 311: Population Studies

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 l , q and e , Description and uses of life table columns.

x x x

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

1. 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.

2. Hinde, A., (1998). “Demographic Method”, Arnold New York.

3. Impagliazo, J. (1993), Deterministic Aspects of Mathematical

Demography, Springer Verlag New York.

4. Jay Weinstein, Vijayan, K. Pillai, (2001) “Demography: The Science of

Population”. Allyn & Bacon.1.

5. Keyfitz, N. (1983) “Applied Mathematical Demography”, Springer

Verlag N.Y.

6. Palmore, J.A; Gardner, R.W. (1994), “Measuring Mortality Increase”;

East West Centre, Honolulu.

7. Pollard, A.H., Yousaf, F & Pollard, G.M. (1982), “Demographic

Techniques”, Pergamon Press, Sydney.

8. Rukanuddin A.R. and Farooqi, M.N.I.., (1988), “The State of

Population in Pakistan – 1987”, NIPS, Islamabad.

9. Govt. of Pakistan (1998), National, Provincial and District census

reports and other supplementary reports with respect to 1998

census; PCO, Islamabad.

10. Pakistan Demographic Survey (2007), Govt. of Pakistan.

11. Publications of population census organizations.

12. United Nations (1990), “World Population Monitoring 1989”, UNFPA.

13. United Nations (1998), “World Population Assessment”, UNFPA; New

York.

14. United Nations (1996), “Added years of Life in Asia” , ESCAP; U.N.,

Thailand.

15. Haupt, A., Kane, T. T., and Haub, C. (2011) PRB’s Population

Handbook.

STAT- 401: Statistical Inference-I

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:

1. Bickel, P.J., and Docksum, K.A. (2005), Mathematical Statistics, Vol

I, Prentice Hall, N.J., 2nd ed.

2. Hogg, R.V. and Craig, A.T. (1996). “Introduction to Mathematical

Statistics”. Prentice Hall, New Jersey.

3. Lindgren, B.W. (1998). “Statistical Theory”. Chapman and Hall, New

York.

4. Mood, A.M., Graybill, F.A. and Boss, D.C. (1997). “Introduction to the

Theory of Statistics”. McGraw Hill, New York.

5. Rao, C.R., (2009). “Linear Statistical Inference and its Applications”,

John Wiley, New York.

6. Rohatgi, V. K. (1984) Statistical Inference. Courier Dover

Publications.

7. Stuart, A. and Ord, J.K. (2009). Kendall’s’ “Advanced Theory of

Statistics” Vol. II. Charles Griffin, London.

8. Zacks, S. (1973), “Parametric Statistical Inference”, John Wiley, New

York.

STAT- 403: Multivariate Analysis

Introduction to Multivariate data analysis, Basics of matrix and vector

algebra, Geometry of vectors and sample, Expectation of sample mean,

covariance matrix, linear combination of variables, Generalized variance,

Multivariate Normal Distribution: Multivariate Normal density and its

properties, Sampling distribution of sample mean vector and covariance

matrix including their large sample behavior. Assessing normality,

transformation to make non-normal data to normal, Outliers, Hotelling’s T2

and likelihood ratio tests, Inferences about mean vector(s), Confidence

regions and simultaneous comparisons of component means, Multivariate

Linear Regression.

Principal components analysis, Factor Analysis, Discrimination and

Classification, Cluster Analysis

Recommended Books:

1. Afifi, A. A. and Clark Virginia (1984). Computer Aided Multivariate

Analysis, Lifetime learning publications, Belmont California.

2. Anderson, T.W. (2003). An Introduction to Multivariate Statistical

Analysis, John Wiley, New York.

3. Chatfield, C. and Collins, A.J. (1980). Introduction to Multivariate

Analysis, Chapman and Hall, London.

4. Everett, B.J. (1974). Cluster Analysis, McGraw-Hill, New York.

5. Flurry B. (1997) A First Course in Multivariate Statistics, Springer

Valerg, New York.

6. Hair, J.F., Anderson R.E., Jatham, R.L.and Black W.C., (1998).

Multivariate Data Analysis, 5th ed. Pearson Education, Re print 2005,

Asia edition.

7. Johnson, R.A. and Wichern, D.W. Applied Multivariate Statistical

Analysis (6th ed.). Prentice Hall. London.

8. Joseph F. Hair Jr, William C. Black , Barry J. Babin ,Rolph E.

Anderson (2009). Multivariate Data Analysis (7th Edition), Pearson

education Asia Edition.

9. Manly, B.F.J. (1994). Multivariate Statistical Methods, A Primer 2nd

Edition, Chapman and Hall, London.

10. Mardia, K.V., Kent, J.T. and Bibby, J.M. (1979). Multivariate

Analysis, Academic Press, London.

11. Morrison. F. (1990). Multivariate Statistical Methods, McGraw-Hill,

New York.

12. Raykov, T. and Marcoulides, G. A. (2008) Introduction to Applied

Multivariate Analysis. Tylor & Francis.

13. Rechner, A. C. (2002) Methods of Multivariate Analysis. Wiley.

14. Sharma, S. (1996), Applied Multivariate Techniques, John Wiley and

Sons, New York.

15. Tabachnick, B.G and Fidell, L.S. (1996), Using Multivariate

Statistics, 3rd ed. Harper Collins College Publishers.

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:

1. Hogg, R.V. and Craig, A.T. (1996). “Introduction to Mathematical

Statistics”. Prentice Hall, New Jersey.

2. Hirai, A. S. (2012) Estimation of Parameters. Ilmi Kitab Khana

Lahore.

----------------------- Page 32-----------------------

3. Lehman, E.L. (2008). “Testing Statistical Hypotheses”. Springler -

Volga, New York.

4. Lindgren, B.W. (1998). “Statistical Theory”. Chapman and Hall, New

York.

5. Mood, A.M. Gray Bill, F.A. and Boss, D.C. (1997). “Introduction to

the Theory of Statistics”. McGraw Hill, New York.

6. Rao, C.R., (2009). “Linear Statistical Inference and its Applications”,

John Wiley, New York.

7. Stuart, A and Ord, J.K. (2009). Kendall’s’ “Advanced Theory of

Statistics” Vol. II. Charles Griffin, London.

8. Welish, A. H. (2011) Aspects of Statistical Inference. Wiley.

9. Zacks, S. (1973), “Parametric Statistical Inference”, John Wiley, New

York.

STAT- 422: RESEARCH PROJECT / INTERNSHIP

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ELECTIVE COURSES

STAT- 405: Research Methodology

Definition of Research, Types of Research: Selection of Problem, Search

of References, Formation of Hypothesis and Procedure for its Testing,

Research Design, Planning of Experiments to Test Hypothesis Objectivity,

Principals of Experimental Design, Steps in Experimentation, Designing

Questionnaire, Collection of Data, Data Analysis to Determine, Functional

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.

PRACTICAL: Survey of Literature on a Given Topic, Collection of

References from Various Sources. Collection of Primary and Secondary

Data, Arrangement of Primary and Secondary Data, Preparation of

Scientific Report for Publication, if Possible

Pre-Requisite: STAT-304

Recommended Books:

1. Gimbaled, J. and W.S. Acuter (1988) “MLA handbook for Writers of

Research Papers”, McGraw the Modern Language Association of

America.

2. Hashmi, N. (1989) “Style Manual of Technical Writings”,

USAID/NARC, Islamabad.

STAT-406: Operations Research

History and definition of Operation Research, 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,

Inventory models, Dynamic programming and simulation models

Recommended Books:

1. Bazarra, N.M., Jarvis J.J. and Sherali, H.D. (1990) “Linear

Programming and Network Flows”, John Wiley & Sons, 2nd ed.

----------------------- Page 34-----------------------

2. Bronson, R. (1983). “Operations Research – Schaums’ Outline

Series” – McGraw-Hill.

3. Gupta, P.K. & Hira, D.S. (2008). “Operations Research”. (7th ed.) S.

Chand & Co., New Delhi.

4. Hillier, F.S. and Lieberman G. J. (2005). “Introduction to Operations

Research”, (8th ed.)Holden Day.

5. Ravindran, A., Philips, D.J and Silberg, J.J. (2007). “Operations

Research: Principles and Practice” (2nd ed.) John Wiley.

6. Taha, H.A. (2002) Operations Research. Macmillan. London

STAT- 407: Stochastic Processes

Introduction, Generating Functions, Laplace Transforms, Difference

Equations, Differential-Difference Equations, Introduction to Stochastic

Processes. The Random Walk in one and two Dimensions, The Classical

Gambler’s Ruin Problem, Expected Duration of the Game

Markov Chains: Definition. Higher Transition Probabilities, Classification of

States and Chains, Markov processes with Discrete State Space, Poisson

Process and its Generalization, Pure Birth and Death Processes, Markov

Processes with Discrete State Space (Continuous Time Markov Chains),

Markov Processes with Continuous State Space. Introduction to Brownian

motion

Recommended Books

1. Cox, D.R.and Miller H.D. (1984). “The Theory of Stochastic

Processes”, Chapman and Hall, London.

2. Grimmet G. and Stirzaker D. (2001): Probability and Random

Processes, Oxford University Press.

3. Hole, P.G., Port, S. and Stone, C.L. (1984). “An Introduction to

Stochastic Process”, John Wiley, New York.

4. Karlin, S.A. and Taylor H.M. (1984). “A first course in Stochastic

Process”, Academic Press London.

5. Medhi, J. (1982), “Stochastic Processes”, Wiley Eastern Ltd.

6. Ross, S. M. (2006). “Stochastic Process”, John Wiley, New York.

7. Srinivasin, S.K. and Mehta, K.M. (1988). “Stochastic Processes”.

Tata McGraw-Hill.

----------------------- Page 35-----------------------

STAT- 408: Reliability Theory

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:

1. Achintya Haldar, Sankaran Mahadevan (2000). Reliability

Assessment Using Stochastic Finite Element Analysis”.

2. Crowder, M.J. (1994). “Statistical Analysis of Reliability Data”.

3. Gertsbakh, I.B. (1989). “Statistical Reliability Theory”. Marcel

Decker. New York.

4. Gertsbakh, I. Reliability theory : with applications to preventive

maintenance Publisher: New Delhi : Springer, 2009

5. Lawless, J.F. “Statistical Model and Methods for Lifetime Data”.(2nd

ed.)

6. Lee, J. Bain, Bain Bain, (1991). “Statistical Analysis of Reliability and

Life-Testing Models”.

7. Mann, N.R., Scheefer, R.E. and Singapoor walla, N.D. (1974).

Methods for Statistical Analysis of Reliability , John Wiley & Sons.

STAT- 409: Time Series Analysis

Time series analysis: concepts, 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

----------------------- Page 36-----------------------

Recommended Books:

1. Andy, P, West M. and Harrison, P. J. (1994). Applied Bayesian

Forecasting and Time Series Analysis, Chapman & Hall New York.

2. Bovas, A. and Johannes, L. (1983), Statistical Methods for

Forecasting, John Wiley. New York

3. Box, G.E.P. and Jenkins, G.M., and Reinsel G. C. (2008) Time

Series Analysis: Forecasting and Control, San Francisco.

4. Brock well P.J. and Davis R.A. (1991). Time Series Theory and

Methods, Springer Verlag New York.

5. Chatfield, C. (1996). The Analysis of Time Series: An Introduction,

Chapman and Hall, London.

6. Chatfield C. (2003): The Analysis of Time Series: An Introduction,

Taylor & Francis, NY, USA.

7. Cox, D. R., Hinckley D.V. and Nielsen O.E.B. (1996). Time Series

Models - In Econometrics, finances and other fields; Chapman &

Hall, London.

8. Diggle, P.J. (1990), Time Series: A Biostatistical Introduction,

Clarendon Press, Oxford.

9. Jonathan D. C. and Kung-Sik C. (2008): Time Series Analysis with

Applications in R, Springer, USA.

10. Hamilton J. D. (1994): Time Series Analysis, Princeton University

Press, UK.

11. Harvey, A.C. (1990). Forecasting Structural Time Series Models and

the Calamander, Cambridge University Press, Cambridge.

12. Peter J. B and Richard A. D (2002): Introduction to Time Series and

Forecasting, Second Edition, Springer, USA.

13. Priestley, M.B. (1981) Spectral Analysis and Time Series, Academic

Press, London.

STAT- 410: Decision Theory

The nature and concept of loss functions, parameters, decisions and

sample spaces, Risk and average loss, Admissibility and the class of

admissible decisions, Minimax principle and its application to simple

decision problems, linear and quadratic losses and their uses in problems

of estimation and testing hypotheses. Asymptotically minimax procedure,

Prior distributions and conjugate priors, Bayes’ decision procedure.

Admissibility of Bayes’ and minimax procedures. Game theory

----------------------- Page 37-----------------------

Recommended Books:

1. Berger, J. O. (1985). “Statistical Decision Theory & Bayesian

Analysis”, Springer Verlag.

2. Blackwell, D. and Graphic, M.A. (1966). “Theory of Games and

Statistical Decision”, John Wiley, New York.

STAT- 411: Robust Methods

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, Outliers and influential observations, Outliers in Regression analysis

Recommended Books:

1. Hamper, T.R. Brochette, E.M. Rousseau, P.J. and Satchel, W.A.

(1986). “Robust Statistics”, “The approach Based on Influence

functions”, John Wiley New York.

2. Hosmer D. W. and Lemeshow S. (2008): Applied Survival Analysis,

Wiley Interscience, USA.

3. Huber, P.J. (1981). “Robust Statistics”, John Wiley, New York.

4. Olive D. J. (2007): Applied Robust Statistics, Southern Illinois

University Department of Mathematics.

5. Rousseau, P.J. and Leroy, A.M. (1987). “Robust Regression and

outlier detection”, John Wiley. New York.

STAT- 412: Official Statistics

Official Statistics, Statistical system and international standards, set up of

national statistical organization 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, Measurement of

Income Distribution, Prices and price mechanisms. Deflation and Inflation

of series, Industrial quantum index, National sample surveys and censuses

conducted in Pakistan.

----------------------- Page 38-----------------------

Note: Visit of major Statistical Organizations should be a part of the

course. Alternatively, the department may invite experts from various

statistical organizations.

Recommended Books:

1. 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.

2. NIPA (1962) “Administrative uses of Statistics” , NIPA Res. Sr.No.2

Karachi.

3. Statistical Institute for Asia & Pacific SIAP (1984). “ Training of

Trainers in Statistical Operations and Procedures” Part-I, II UNDP,

Tokyo.

4. Statistics Division (1979). “Retrospect, Perspective and Prospect”,

Islamabad.

5. Statistics Division, “Activity Report” (1988-89).Government of

Pakistan, Islamabad.

6. Various Publications of PBS, State Bank of Pakistan, Ministry of

Finance, etc.

7. Zarkovich S.S. (1966) “Quality of Statistical Data, Food and

Agricultural Organization”, The U.N. Rome.

8. Statistics Reorganization Act 2011

STAT- 413: Survival Analysis

Special features of Survival data: Patient time and study time, Survival

function and hazard function, Time dependent and censored survival data.

Nonparametric procedures: Estimation of Survival function, hazard

function, median and percentiles of Survival times. Confidence interval and

comparison of group; stratified and log-rank tests for trend, Modeling of

Survival data; Hazard function modeling; its tests and confidence interval,

The Weibull model for survival data, Exploratory data analysis and other

models, Sample size requirement for survival study, Use of software for

Survival analysis

Recommended Books:

1. Burkett, M. (1995). “Analyzing Survival Data from Clinical Trials and

Observational Studies”; John Wiley New York.

2. Collett, D. (1994). “Modeling Survival Data in Medical Research”.

Chapman & Hall, London.

----------------------- Page 39-----------------------

3. Cox, DR. and Oakes, D. (1984). “Analysis of Survival Data” ;

Chapman & Hall London.

4. Eland Johnson, R. C. and Johnson N. L. (1989), “Survival Models &

Data Analysis”. John Wiley N.Y.

5. Lee, E.T. (1992). “Statistical Methods for Survival Data Analysis”;

John Wiley. N.Y.

6. Lee, E.T. (1997). “Applied Survival Analysis”, John Wiley and Sons,

New York.

7. Muller, R.G. and Xian Zhou (1996). “Survival Analysis with long-term

Survivors”, John Wiley. New York.

8. Parmer M.K.B. & Macklin D. (1995). “Survival Analysis: A Practical

Approach ”; John Wiley New York.

9. Turkey, J. (1987). “Exploratory Data Analysis”, John Wiley, New

York.

STAT- 414: Biostatistics

Definition of Biostatistics, type of variables and observations in biological,

health and medical sciences, Uniqueness in terms of behaviour of

variables their domain, and units; Categorical, numerical and censored

data. Populations, Target populations and sampled Population: Role of

sampling in biostatistics, Size of samples of various types of studies,

Proportions, rates and ratios; incidence, prevalence and odds.

Distributional behaviour of biological variables (Binomial, Poisson and

Normal), Role of transformation for analysis of biological variables, Probit

and Logit transformations and their analysis, p values, its importance and

role, Confidence Interval in simple and composite hypothesis testing

Recommended Books:

1. Alfassi Z. B., Boger, Z. and Ronen, Y. (2005): Statistical Treatment

of Analytical Data, Blackwell Science, USA.

2. Altman, G. (1991). “Practical Statistics for Medical Research”.

Chapman & Hall, London.

3. Ahmad, M., Ahmad, A., and Hanif, M. (2004) Manual of Statistics for

Medical Sciences. ISOSS Publications Lahore.

4. Daniel, W.W. (2010). “Biostatistics: A Foundation for the Health

Sciences”, 6th Edition, John Wiley, New York.

5. Diggle, J. P., Liang, Kung-Yee and Zeger, S. L. (1996). “Analysis of

Longitudinal Data”, Clarendon Press, Oxford.

6. Dunn, G. and Everit, B. (1995). “Clinical Biostatistics”, Edward

Arnold, London.

----------------------- Page 40-----------------------

7. Hanif M., Munir A. and Aftab M. A. (2006): Biostatistics for Health

Students with Manual on Software Applications, ISOSS Publication.

8. Harris, E. K. and Albert, A. (1991). “Survivorship Analysis for Clinical

Studies”. Marcel Decker, New York.

9. Lawless, J. F. (1982). Statistical Models and Methods for Life Time

Data. John Wiley, New York.

10. Lee, E.T. (1992). “Statistical Methods for Survival Data Analysis”, 2nd

Edition, John Wiley, New York.

11. Rosner, B. (2006). “Fundamentals of Biostatistics”, Duxbury Press.

12. Shoukri, M. M. & Pause, C. A. (1999). “Statistical Methods for Health

Sciences”. 2nd Edition, CRC Press, Florida.

13. Zar, J. (2000). “Biostatistical Analysis”, 5th Edition, John Wiley and

Sons.

14. Zolman, J.F. (1993). “Biostatistics: Experimental Design and

Statistical Inference”, Oxford University Press, New York.

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; artificial neural networks and

extensions of regression models, regression trees. Association rules and

prediction; applications to electronic commerce

Recommended Books

1. Benson and Smith, S.J. (1997). “Data Warehousing, Data Mining’,

and OLAP. McGraw-Hill.

2. Bramer M (2007): Principles of Data Mining. Springer-Verlag London

Limited UK.

3. Breiman, L. Friedman, J.H. Olshen, R.A. and Stone, C.J. (1984).

“Classification and Regression Trees” Wadsworth and Brooks/Cole.

4. Han, J., Kamber, J. Pei, J., and Burlington, M. A. (2012) Data

mining: concepts and techniques. Haryana, India.

5. Han, J. and Camber, M. (2000). Data Mining; “Concepts and

Techniques”. Morgan Gaufmann.

----------------------- Page 41-----------------------

6. Mitchell, T.M. (1997). “Machine Learning”. McGraw-Hill.

7. 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.

8. Ripley, B.D. (1996). “Pattern Recognition and Neural Networks”.

Cambridge University Press.

9. Suh, S. C. (2012) Practical applications of data mining. Suh.

Publisher

10. Tan P., Steinbach M. & Kumar V. (2006): Introduction to Data

Mining. Addison Wesley, New York .

STAT- 416: Actuarial Statistics-I

Introduction to actuarial Statistics, Utility theory, insurance and utility

theory, models for individual claims and their sums, survival function,

curate future lifetime, force of mortality

Life table and its relation with survival function, examples, assumptions for

fractional ages, some analytical laws of mortality, select and ultimate

tables.

Multiple life functions, joint life and last survivor status, insurance and

annuity benefits through multiple life functions, evaluation for special

mortality laws

Multiple decrement models, deterministic and random survivorship groups,

associated single decrement tables, central rates of multiple decrement,

net single premiums and their numerical evaluations.

Distribution of aggregate claims, compound Poisson distribution and its

applications

Recommended Books:

1. Bowers, N.L. Gerber, H.U. Hickman, J.C. Jones, D.A. and Nesbitt, C.J.

(1997). “Actuarial Mathematics”, Society of Actuarial, Ithaca, Illinois,

U.S.A

2. Dkkson, M. R., Hardy, H, Wates (2009) Actuarial Mathematics for Life

Contingent Risks. Cambridge.

3. Neill, A. (1977). “Life Contingencies”, Heineman.

4. Polard, B., John, H. (1980) Analysis of Mortality and Actuarial

Statistics. Faculty & Institute of Actuarial Sciences U.K.

----------------------- Page 42-----------------------

5. Spurgeon, E.T. (1972), “Life Contingencies”, Cambridge University

Press.

STAT- 417: Actuarial Statistics-II

Principles of compound interest: Nominal and effective rates of interest and

discount, force of interest and discount, compound interest, accumulation

factor, continuous compounding.

Life insurance: Insurance payable at the moment of death and at the end

of the year of death-level benefit insurance, endowment insurance,

deferred insurance and varying benefit insurance, recursions, commutation

functions.

Life annuities: Single payment, continuous life annuities, discrete life

annuities, life annuities with monthly payments, commutation functions,

varying annuities, recursions, complete annuities-immediate and

apportionable annuities-due.

Net premiums: Continuous and discrete premiums, true monthly payment

premiums, apportionable premiums, commutation functions, accumulation

type benefits.

Payment premiums, apportionable premiums, commutation functions,

accumulation type benefits.

Net premium reserves : Continuous and discrete net premium reserve,

reserves on a semi-continuous basis, reserves based on true monthly

premiums, reserves on an apportionable or discounted continuous basis,

reserves at fractional durations, allocations of loss to policy years,

recursive formulas and differential equations for reserves, commutation

functions.

Some practical considerations: Premiums that include expenses-general

expenses types of expenses, per policy expenses.

Claim amount distributions, approximating the individual model, stop-loss

insurance.

Recommended Books:

1. Borowiak, D. S., Shapiro, A. F. (2003) Financial and Actuarial

Statistics: An Introduction. CRC Press.

2. Bowers, N.L. Gerber, H.U. Hickman, J.C. Jones, D.A. and Nesbitt,

C.J. (1986) “Actuarial Mathematics”, Society of Actuaries, Ithaca,

Illinois, U.S.A. Second Edition (1997).

----------------------- Page 43-----------------------

3. Corazza, M. and Claudio, P. (2010) Mathematical and Statistical

Methods for Actuarial Sciences and Finance. Springer.

4. Neill, A. (1977). “Life Contingencies”, Heinemann.

5. Spurgeon, E.T. (1972). “Life Contingencies”, Cambridge University

Press.

STAT- 418: Mathematical Modeling and Simulation

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 variates and antithetic

variables.

Recommended Books:

1. Bernard P Autor Zeigler, Herbert Praehofer, Tag Gon Kim (2000)

Theory of Modeling and Simulation

2. Daniel P. M, Maynard T. (2006): Mathematical Modeling and

Computer Simulation, Thomson Brooks/Cole

3. Fishman, G.S. (1996). Monte Carlo: “Concepts, Algorithms, and

Applications”, (Springer).

4. Ripley, B.D. (1987) “Stochastic Simulations” ( Wiley)

5. Ross, S.M. (2002). “Simulation” ( Third Edition) (Academic)

6. Rubinstein, R.Y. (1981). “Simulation and the Monte Carlo Method”,

(Wiley).

7. Velten, K. (2009): Mathematical modeling and simulation, Wiley

VCH, Germany

STAT- 419: Categorical Data Analysis

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, Exact

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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:

1. Alan Agresti (2012) Categorical Data Analysis (3rd edition). Wiley.

2. Alan Agresti (2007) An Introduction to Categorical Data Analysis (2nd

edition). John Wiley & Sons.

3. Chap T. Le (1998) Applied Categorical Data Analysis. Wiley

4. Collett D. (2003) Modeling Binary Data. Champman and Hall/CRC.

5. Hosmer D. W., Lemeshow S. (2004) Applied Logistic Regression.

John Wiley & Sons.

6. Lloyd C. J. (1999) Statistical Analysis of Categorical Data. Willey

7. Powers D. A., and Yu Xie (2008) Statistical Methods for Categorical

data analysis (2nd edition). Emerald Group publishing.

8. Ronald C. (1997) Log-linear models and logistic regression (2nd

edition). Springer.

9. Simonoff J. S. (2003) Analyzing Categorical Data. Springer

STAT- 422: Bayesian Inference

Conditional Probability, Prior information, Prior distributions, Methods of

elicitation of prior distributions, Posterior distributions: The posterior

means, medians (Bayes estimators under loss functions) and variances of

univariate and bivariate posterior distributions, Non-informative priors:

Methods of elicitation of non-informative priors, Bayesian Hypotheses

Testing: Bayes factor; The highest density region; Posterior probability of

the hypothesis.

Recommended Books:

1. Berger, J.O., Statistical Decision Theory and Bayesian Analysis (2nd

Ed.), New York, Springer Verlag (1985).

2. Bernardo, J. M. & Smith, A.F.M., Bayesian Theory, John Wiley, New

York (1994).

3. Box, G.E. P & Tiao, G. C. Bayesian Inference in Statistical Analysis,

Reading Addison-Wesley (1973).

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4. Introduction to Bayesian Statistics by William M. Bolstad (2004)

5. Lee, P.M. Bayesian Statistics, an Introduction, Oxford University

Press, New York (1991).

6. O.Hagan A. Kendall’s Advanced Theory of Statistics (Vol.2B),

Bayesian Inference, Cambridge, The University Press (1994).

STAT- 423: Statistical Quality Control

Concept of quality control and Quality assurance, Total Quality

Management (TQM) Statistical Methods in Quality Improvement, Statistical

Process Control (SPC), Statistical Quality Control (SQC), Shewhart control

charts: philosophy, construction, advantages. CUSUM and moving

average control charts: Average Run Length (ARL); Fast Initial Response

(FIR). ARL and FIR for control charts

Process capability analysis: Process improvements using design of

experiments.

Acceptance sampling for attributes and variables, Acceptance sampling

plans: Single, double, and multiple sampling plans with their O.C. curves,

Military Standard 501 Sampling Plans. Introduction to ISO- 9000 and ISO-

14000 series

Pre-Requisite: STAT-301

Recommended Books:

1. Banks, J. (1989). “Principles of Quality Control”. John Wiley, New

York.

2. Feigenbaum, A.V. (1986). “Total Quality Control”. McGraw-Hill, New

York.

3. Juran, J.M. and Guyana, F.K. (1988). “Juan’s Quality Control

Handbook”. McGraw Hill New York.

4. Miltag H. J. and Rinne H. (1993). “Statistical Methods of Quality

Assurance” , Chapman & Hall, London.

5. Montgomery, D.C. (2013). “Introduction to Statistical Quality

Control”. McGraw Hill, New York.

6. Nelson, W. (1990). “Accelerated Testing” . John Wiley, New York.

7. Ryan, T.P. (1989). “Statistical Methods for Quality Improvement”.

John Wiley, New York.

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Recommendations

The following recommendations were made by the committee to enhance

the teaching and learning of Statistics:

1. Departments of Statistics in the universities should make efforts to

interact with national and international statistical organizations such

as PBS, industry and other users of statistics in the public and

private sector.

2. Internship should be funded by the HEC and/or other funding

agencies, and offered to the students.

3. All universities’ departments should develop and maintain an

internship / career services department to facilitate the internship

students of Statistics.

4. Most of the courses may be taught using statistical packages.

5. Since there is a shortage of highly qualified statisticians in Pakistan.

Therefore, allocating extra quota for statistics students to pursue

higher education is needed.

6. The committee strongly recommends the creation of “Department of

Biostatistics” for teaching and research guidance at all medical

colleges/universities and the posts of biostatisticians in all

hospitals/other institutions.

7. Practicum conducted during the course work should be in the form of

case studies. The data published by different organizations may be

used in such case studies.

8. A course on Statistics may be added in curriculum of FSc (Pre-

Medical & Pre-Eng.) to prepare students for their professional

education.

9. The department of Statistics in each university may establish a

statistics consultancy center to attract potential researchers. HEC

should provide technical and financial support to these research

cells.

10. Refresher courses for the faculty should be regularly arranged by the

HEC.

11. HEC should support universities for the development of computer

labs, departmental libraries, students and staff participation in

seminars, workshops, and conferences.

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12. The department websites should be updated on a regular basis so

that research interests of the faculty may become public.

13. PGD (Post Graduate Diploma) / Short courses should be offered by

the universities/department of Statistics to the non-statisticians.

14. Professional ethics should be an integral part of the training of

students at both the undergraduate and graduate level.

15. Since 4 year BS Programme is equivalent to old M.Sc. Programme

in Statistics, therefore, the relevant recruitment rules for the post of

BPS-17 may be amended by the concerned departments (FPSC,

Establishment Division) and B.S. (Four year Programme) may be

added in the eligibility criteria for the posts.

16. The department of Statistics in each university should make concrete

efforts for establishing university-industry linkages for MS level

research.

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Annexure “A”

COMPULSORY COURSES IN ENGLISH FOR BS

(4 YEAR) IN BASIC & SOCIAL SCIENCES

English I (Functional English)

Objectives: Enhance language skills and develop critical thinking.

Course Contents

Basics of Grammar

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MODEL SCHEME OF STUDIES FOR BS (4-YEAR) IN STATISTICS