BD4008 Statistics for Business Analytics Syllabus:

BD4008 Statistics for Business Analytics Syllabus – Anna University PG Syllabus Regulation 2021

COURSE OBJECTIVES:

 To provide the required skill to apply the statistical tools in engineering Problems.
 To introduce the basic concepts of Time Series and Estimations.
 To acquaint the knowledge of Statistical Inference and Decision Theory.
 To provide the basic tools of Statistics for data analysis and Decision making on the sampling and inference.

UNIT I INTRODUCTION TO TIME SERIES

Time Series: Meaning And Need Of Time Series Analysis, Components Of Time Series, Additive And multiplicative Model, Utility Of Time Series. Methods Of Determining Trends. Components Of Timeseries, Smoothing Auto Correlation, Stationarity, Concepts Of AR, MA, ARMA & ARIMA Models with Illustrations.

UNIT II ESTIMATION

Methods of estimation: Random samples, sampling distributions of estimators, Methods of moments, Unbiasedness: Unbiased estimator, Illustration of unbiased estimator for the parameter and parametric function. Definitions of Consistency, Sufficient condition for consistency, concept of efficiency and sufficiency. Neyman- Factorization theorem (without proof), concept of likelihood function, Maximum Likelihood, Properties of MLE (without proof), Estimation of the parameters of normal distribution and other standard distributions by MLE.

UNIT III STATISTICAL INFERENCE AND DECISION THEORY

Statement and proof of Cramer Rao inequality. Definition of Minimum Variance Bound Unbiased Estimator (MVBUE) of φ(θ), (statement only). Rao-Blackwell theorem, Lehmann-Scheffe theorem. Definition of MVUE, Procedure to obtain MVUE (statement only), examples. Minimum Variance Unbiased Estimator (MVUE) and Uniformly Minimum Variance Unbiased Estimator(UMVUE). Basic elements of Statistical Decision Problem. Expected loss, decision rules(nonrandomized and randomized), decision principles (conditional Bayes, frequentist), inference as a decision problem, optimal decision rules. Bayes and minimax decision rule. Admissibility o fminimax rules and Bayes rules.

UNIT IV REGRESSION AND RELIABILITY

Multiple linear regression, forward, backward & stepwise regression, Logistic Regression. Reliability of system of independent components, association of random variables, bounds on system reliability, improved bounds on system reliability using modular decompositions. Replacement policy comparisons, preservation of life distribution classes under reliability operations. Reversed hazard rate, cumulative reversed hazard function, relation between hazard function and reversed hazard function. Reversed lack of memory property.

UNIT V STATISTICAL QUALITY CONTROL

Meaning and purpose of Statistical quality control, Concept of process control, product control, assignable causes, chance causes and rational subgroups. Control charts and their uses, Choice of subgroup sizes, Construction of control chart for (mean), R (range), s (standard deviation), c (no.of defectives), p (fraction defectives) with unequal subgroup size. Interpretation of non-random patterns of points. Modified control chart. CUSUM Chart. Consumer’s risk, producer’s risk, OCcurve, acceptance sampling plan by attributes and variables. Concept of Six Sigma.

TOTAL:45 PERIODS

COURSE OUTCOMES :

By the end of the course the students will be able to
CO1: Perform time series analysis of data.
CO2:Apply the concept of Point estimation by Method of moments and Maximum likelihood estimation.
CO3:Evaluate the regression and reliability for the statistical sampling data.
CO4:Apply various estimators for the statistical concepts.
CO5:Apply various techniques in quality control and acceptance sampling.

REFERENCES:

1. Johnson, R.A., Miller, I and Freund J., “Miller and Freund‘s Probability and Statistics for Engineers”, Pearson Education, Asia, 8th Edition, 2015.
2. Barlow, R. E. and Proschan F. (1996). Mathematical Theory of Reliability. John Wiley.
3. Statistical Inference: P. J. Bickel and K. A. Docksum, 2ndEdition, Prentice Hall
4. Duncan A.J. (1974): Quality Control and Industrial Statistics, IV Edition, Taraporewala and Sons.
5. M. Mitzenmacher and E. Upfal. Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, 2005.
6. Devore. J.L., “Probability and Statistics for Engineering and the Sciences‖, Cengage Learning, New Delhi, 8th Edition, 2014.
7. Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining, “ Introduction to Linear Regression Analysis”,Wiley, 6th Edition, 2021.
8. Chris Chatfield “The Analysis of Time Series: An Introduction”, Chapman & Hall/CRC,Sixth Edition, 2003.
9. George Casella, Roger L. Berger, “Statistical Inference”, 2nd ed., Thomson Learning,2007.
10. Mukhopadhay, Parimal, ”Theory and Methods of Survey Sampling”, Prentice Hall,2008.
11. Tobias, P. A. and Trindane, D. C, “Applied Reliability”, Second edition, CRC Press,1995.
12. Rao, C.R.,” Linear Statistical Inference and its Applications”, Wiley Eastern,2009.