1)  Compulsory Courses

2)  Elective Courses

*Part I: Six ideas of sampling methods, sampling distributions of means, t , c2 , F and their large sample approximations . Decision theory approach to one sample and two samples inference.

*Part II: Regression analysis and significance test of regression model. Interpretation of coefficient of determination for full and partial model. Test of simple and multiple correlations.

*Part III: Basic principles in experimental designs, single factor ANOVA (CRD) for balanced and unbalanced cases. Multiple comparisons (tests), comparing treatment with control. Two factor ANOVA (RBD) with missing values, LSD with missing values . Introduction to factorial designs (only for two levels).

*Part IV: Test of Attributes: Goodness of fit, Contingency tables , test of Independence. Some non-Parametric tests. Interval estimation for some Order Statistics.

 References:

1.   Dantel, Wayne.W; Bio-Statistics, A Foundation for Analysis in the health sciences.
2.  Fowler, J & Cohen, L: Practical Statistics for Field Biology .
3.  Schefler W.C.: Statistics for Biological Sciences.
 Walpole R.E; Introduction to Statistics.

* M.Sc. students of Chemical and Biological sciences .

   الانتقال إلى جدول المقررات الدراسية 

Review of symmetric factorial experiments. Algebric representation of main effects and interaction, estimation and analysis of some factorial experiments. Analysis of confounded factorial experiments. Factorial replications. A symmetric factorial experiments. Estimable function and its properties. General linear model of non-full ran . Generalized inverse of matrices. Tests for full and part models. Non-orthogonal designs. Least square estimates and analysis of two-way non-orthogonal designs. General block design. Incomplete block designs. PBIB design. Intra- and block analysis of incomplete block  design. Youden square design. Lattice design. Construction of incomplete block design. Multi-way non-orthogonal designs. Residual effects, Weighing designs. Analysis of covariance with two ancillary variates, covariance and analysis of experiments with missing observations. Random and mixed effect model. Variance component analysis. Response surface design. First order and second order models. Methods of steepestascent. Groups of experiments. Ideas of D-optimality, Rotatibility and connectedness.

References:

1. John, P.W.: Statistical design and analysis of expt.; Macmillan.
2. Graybill, F.A.: An introduction to linear statistical models; Mac Graw Hill.
3. Liner, B.J.: Statistical Principle in expt. design; Mac Graw – Hill.
4. Montgomery, D.C.: Design and analysis of ext.; J. Wiley M.Y.
5. Mayers, R.H.: Response surface Methodology, Allyn and Bacon. Inc. Boston.
6. Raghjararao, D.: Constracution and combinatorial problems in design of expt. ; Wiley

    الانتقال إلى جدول المقررات الدراسية 

Single-stage sampling of unequal clusters: selection of unequal clusters with unequal probability without replacement; Horvitz-Thompson estimator; other methods of estimation; Estimation of standard errors. Sub-sampling: Two-stage and higher-stage sampling with equal clusters; optimum allocation of clusters; sub-sampling with unequal clusters; Multi-stage sampling PSU'S selected with equal and unequal probability with or without replacement; Unbiased and ratio estimates; random group methods, self-weighing estimates; non-linear estimates of standard errors; Stratified multistage sampling. Double Sampling: Use of double sampling for stratification; regression estimators; ratio estimators and PPS estimation; Optimum allocation. Repeated sampling, sampling on two or more occasions. Sources of errors in survey; Non-response and non-sampling error; Interviewer variability; interpenetrating subsamples; error of measurement, Familiarity with large-scale sample survey.

References:

(1) Cochran, W.G.: Sampling techniques; Wiley.
(2) Raj, D.: Sampling theory; MacGraw – Hill.
(3) Kendall and Stuart; Advanced theory of statistics V.3, Charles Griffins.

     الانتقال إلى جدول المقررات الدراسية 

General description of decision problems. Utility and loss function, decision rules, expected utility principle. Simple problem with finite decision and parameter spaces. Problems without prior distribution, Risk function, Dominance, admissibility, Completeness, minimax.Baysian decision rules: Baysian approach for more general problems with application to point estimation, discrimination, hypotheses testing. 2-decision problem with linear loss function. Baysian decision prediction.

References:

1. Ferguson, T.S.: Mathematical statistics. A decision theoretical approach, Academic press, 1967.
2. De Groot, M.H.: Optimal statistical Decision. Mc Graw-Hill 1970.
3. Aitchison, J. and Dunsmore, I.R.: Statistical prediction analysis 1975, Cambridge.

 Introduction reading:

4. Lindly, D.V.: Making decision; Wiley 1971.
5. Lindgren, B.W.: Elementary Decision theory; Mac Millan, 1971.

   الانتقال إلى جدول المقررات الدراسية 

Time series analysis

(3 Cr.)

 A quick review on concepts of time series. Probability models for time series: stochastic processes, Stationary process. Auto correlation function. Auto-regressive processes: MA, AR, ARMA and ARIMA processes. Estimation of parameters of models: Estimation of auto covariance and auto-correlation functions. Estimation of parameters of different auto-regressive processes. Residual analysis. Stationary Processes: Spectral distribution and density function, Spectral analysis - Fourier analysis. Myquist frequency, Perio dogram analysis. Relationship between priodogram and auto correlation functions. Truncated autocorrelation function. First Fourier transforms. Ideas of bivariate time - series: Cross - covariance and cross - correlation functions. Cross spectrum - linear system.

References:

(1) Chatfield, C.: The analysis of time series, An introduction; Chapman & Hall.
(2) Box and Jankins: Time series analysis, Forecasting and control; Hol- den Day.
(3) Kendal, M.G. and Stuart: Advanced Theory of Statistics V.3, Charel- e's Griffin.
(4) Andrson, T.W.: Analysis of time series, Wiley and Sons.

   الانتقال إلى جدول المقررات الدراسية 

2605

Econometrics

(3 Cr.)

 Theory Part: A short review of general linear model where assumptions break down. General linear model with stochastic regression. General linear model with lagged variables: Lagged explanatory variables, lagged dependent variable, Estimation of parameters. Simultaneous Equation Methods: (a) Identification: Simultaneous Equation system, Identification problems. (b) Estimation: Recursive system, Two-stage and three-stage least squares, Limited information (Least variance ratio) Estimators. Applied Part: Income distribution, Demand-supply curves; production and consumption function, Cobb-Web models, Cobb-Douglas production function, CES production function, Input - output analysis.

References:

(1) Johnston, J: Econometric methods, Mc Graw - Hill, N.Y.
(2) Golderger, A.S.: Econometric Theory, John-Wiley and Sons, N.Y.
(3) Leser, C.E.V, Econometric Techniques and problems; Charles Griffin, London.
(4) Klein, L.R.: A text book of Econometrics; Evanston, Row eterson & Co.
(5) Fisher, F.M.: The Identification problem in Econometrics, Mc Graw-Hill, N. Y.

   الانتقال إلى جدول المقررات الدراسية

2606

Probability Theory

(3 Cr.)

Elements of measure theory: Topological space, Fields and Fields of subsets, measurable functions. Measure: Definition and properties, Finite and additive measure, Borel sets, Lebesgue measure, Lebesgue integral, Radon-Mikodyn theorem, Riemann-Stieltjes integral. Probability space, independent events, conditional probability and conditional probability space, Baye's rule.

Random variables: Random variable as a measurable function, independence, Distribution of random variable, Distribution and density functions, Parameters of distribution, Distribution of functions of random variable, Joint and marginal densities, Conditional densities, Convolutions, probability generating function, Characteristic functions. Sequences of random variables: Concepts of convergence, Weak and strong law for independent and identically distributed random variables, Laws of large numbers, Central limit theorem and some of it's extensions, Infinitely divisible and stable distributions.

References

(1) Feller, W.: An introduction to probability theory and it's applications, Vol. II, Wiley.
(2) Cramer, H.: Random variables and probability Distributions, UMIVER. Press Cambridge
(3) Renyi, A.: Probability theory, Morth Holland Pub. Company, Amsterdam.
(4) Fisz; M.: Probability theory and Math. Statistics,  Wiley.
(5) Chung, K.L.: A course in Probability theory, Academic press.
(6) Papoulis, A.: probability, Random variables and Stochastic processes; Mc Graw – Hill.
(7) Burril, C.W.: Measures Integration and probability, Mc Graw – Hill.(8) Parzen, E.: Modern Probability theory and it's applications, J. Wiley.(9) Aram J. Thomsian : The structure of probability and stochastic processes , Mc Graw- Hill .

   الانتقال إلى جدول المقررات الدراسية 

2607

Operations Research

(3 Cr.)

Constrained Optimization: The general mathematical programming problem; Linear programming as a special case, Mathematical formulation of some practical problems as linear programming pros, Graphical solution methods, Canonical and standard of L.P.P.; the simplex method; fundamental properties of solutions, corroboration of extreme points, Simplex algorithm. Duality theory-Writing dual of a L.P.P. and duality relations. The Transportation problem - Description, the transportation table, methods of finding initial basic feasible solutions, the transportation algorithm, degeneracy in T.P., unbalanced T.P. The assignment problem: Nature of the problem, it's mathematical formulation as a linear program, the assignment algorithm, the unbalanced A.P. Advanced topics in programming: Linear factorial programming, Factorial algorithm, Stochastic programming and chance constrained programming, concepts of quadratic, dynamic discrete programming.

References:

(1) Taha,H.A. - Operation research - An introduction , Mac Millan .
(2) Vojda, S. - Mathematical programming, Addison – Wesley.
(3) Kantiswarup -Linear Fractional programming Operations Research, V.13 (1965)  PP 1029 –1036.
(4) Garvin W.W - Introduction to linear Programming, Mc Graw – Hill.(5) Sasiemi,M; Yaspan, A. and Friednien, L.Operational Research (Methods and  Problems) J.Wiley.
(6) Gottfried, B.S. and Weisman, J. - Introduction to Optimization theory; Prentic- Hill .

   الانتقال إلى جدول المقررات الدراسية 

2608

Population analysis

(3 Cr.)

Collection of Census and vital statistics; Errors in census and vital statistics; Fertility and reproduction; Mortality projections and theories; Family formation, Composition and dissolution; Nuptiality; Distribution of population; Growth of population; Population estimates and projection; Health statistics; Morbidity analysis; Epidemeology; Survival analysis.

References:

(1) Demography - P.R. Cox.
(2) Principles of Demography - D.J. Bogne.
(3) Introduction to Demography - Spiegelman.
(4) The study of population - Houser and Duncan.
(5) Health and vital statistics - Bernard Benjamin.

   الانتقال إلى جدول المقررات الدراسية 

2609

Prediction forecasting and control

  (3 Cr.)

Linear least squares prediction problem; Wiener and Kolmogrov methods; applications in standard stationary time series models; extension to filtering theory: recursive relations for predictors; standard forecasting techniques (IWMA, Brown, Holt); control of linear stochastic systems loss functions; Principle of certainty equivalence; Box-Jenkins feedback controllers; optimal regulation; estimation of parameters in linear system; estimation of transfer functions in open and closed loop system.

References:

(1)  ASTROM, K.J.: Introduction to Stochastic Control Theory,
( Academic Press 1971).

(2) BOX, G.: Time Series Analysis, Forecasting and Control, Jenkins, G.M. (Holden-Day, 1970).

(3) WHITTLE, P.: Prediction and Regulation by least-squares methods (English Universities press, 1963).

   الانتقال إلى جدول المقررات الدراسية 

2610

Medical statistics

(3 Cr.)

(1) Methodology and Model Building: Problem solving in human activity system-specifically in health and health care; the role of statistics in evaluating models; types of model; criteria for appropriateness of models. Discussion of journal articles with a health context.

(2) Linear programming: The linear model; primal and dual problems; shadow prices; reduced costs; sensitivity analysis; optimality in medical context. Discussion on the DHSS "Balance of Care" model.

(3) Simulation: Deterministic and probabilistic simulation models. Advantages and disadvantages in their use. Description of model for population cancer screening; it's validity and use in policy formulation; Gaming simulation; Monte-Carlo models; their use in resource allocation in hospital. Discussion of paper concerned with dialysis/renal transplantation.

(4) Drug Evaluation: Phases of investigation, randomized controlled trials, numbers of patients required, treatment allocation and stratification, placebo effects, within-patient comparisons. Statistics in the pharmaceutical industry.

(5) Distribution-Free Methods: Clinical measurement and ordinal scales, distribution free nature of ranks, one-sample and two-sample tests based on ranks, methods using empirical distribution function, comparison with parametric techniques, choice of test for a medical data set.

(6) Utility in Medicine: Utility functions; the fractile technique; utility axioms; application to the measurement of illness; individual utilities with respect to treatment options (e.g. 5 year survival lung cancer); community utilities providing an objective function for health services; benefit and cost assessment of health policy options. Discussion of journal articles.

(7) Analysis of Survival Data: Patient survival studies and " censored " observations; survivorship function and hazard functions; product-Limit estimate of survival curve; clinical life tables; estimation and inference in the exponential distribution; other distributions of survival time; use of concomitant information and regression models.

References:

(1) GROSS, A.J. and CLARK, V.A.: Survival Distribution: Reliability Applications in the Biomedical Sciences (Wiley 1975).

(2) PETO, R., PIKE, M.C. et. al.: Design and analysis of randomized clinical trials requiring prolonged observation of each patient. I.introduction and design. Br.J. cancer (1976) 34, 585.

(3) De NEUFVILLE, R. and STAFFORD, J.H.: System analysis for engineers and managers ( McGraw-Hill 1971).

   الانتقال إلى جدول المقررات الدراسية