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Statistical Methods for Scientists and Engineers

Statistical Methods for Scientists and Engineers. Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur. This course introduces some important topics in statistical methods used in science and engineering. Topics include: basic concepts of probability and distributions; parametric methods - point estimation, interval estimation, testing of hypotheses; multivariate analysis - multivariate normal distribution, Wishart and Hotelling's T-squared Distributions and their applications, classification of observations, principal component analysis; nonparametric methods - empirical distribution function, single sample problems, problems of location, Wilcoxon signed rank statistics, two sample problems, Mann-Whitney-Wilcoxon tests, scale problems, Kolmogorov-Smirnov two sample criterion, Hoeffding's U-statistics. (from nptel.ac.in)

Foundations of Probability


Review of Probability and Distributions
Lecture 01 - Foundations of Probability
Lecture 02 - Laws of Probability
Lecture 03 - Random Variables
Lecture 04 - Moments and Special Distributions
Lecture 05 - Moments and Special Distributions (cont.)
Lecture 06 - Special Distributions (cont.)
Lecture 07 - Special Distributions (cont.)
Lecture 08 - Sampling Distributions
Parametric Methods
Lecture 09 - Point Estimation: Unbiasedness, Consistency, UMVUE
Lecture 10 - Point Estimation: Completeness, Method of Moments, Maximum Likelihood
Lecture 11 - Point Estimation: Properties of Maximum Likelihood Estimation, Method of Scoring
Lecture 12 - Interval Estimation: Confidence Intervals
Lecture 13 - Interval Estimation: Confidence Intervals for proportions
Lecture 14 - Testing of Hypotheses
Lecture 15 - Testing of Hypotheses (cont.)
Multivariate Analysis
Lecture 16 - Multivariate Normal Distribution
Lecture 17 - Multivariate Normal Distribution and its Properties
Lecture 18 - Multivariate Normal Distribution and its Properties (cont.)
Lecture 19 - Random Sample from a Multivariate Normal Population, Noncentral Chi-squared Distribution
Lecture 20 - Wishart and Hotelling's T-squared Distributions and their Applications
Lecture 21 - Wishart and Hotelling's T-squared Distributions and their Applications (cont.)
Lecture 22 - Multivariate Central Limit Theorem, Problem of Classification of Observations
Lecture 23 - Classification of Observations (cont.)
Lecture 24 - Classification Procedures for Two Multivariate Normal Populations
Lecture 25 - Classifying an Observation into One of Two Multivariate Normal Populations
Lecture 26 - Classifying an Observation into One of Several Populations
Lecture 27 - Principal Component Analysis
Nonparametric Methods
Lecture 28 - Distribution-free Methods, Order Statistics
Lecture 29 - Order Statistics (cont.)
Lecture 30 - Bounds on Expected Values, Asymptotic Distributions of Order Statistics
Lecture 31 - Quantiles, Tolerance Intervals, Coverages, Empirical Distribution Function
Lecture 32 - Empirical Distribution Function (cont.)
Lecture 33 - Empirical Distribution Function (cont.), Prediction Intervals
Lecture 34 - Goodness of Fit Test, Kolmogorov?Smirnov One Sample Statistics, Single Sample Location Problems
Lecture 35 - Single Sample Location Problems: Wilcoxon Signed-rank Statistics
Lecture 36 - Single Sample Location Problems (cont.), Intro to Two Sample Problems
Lecture 37 - Two Sample Problems (cont.)
Lecture 38 - Mann-Whitney-Wilcoxon Test, Scale Problems
Lecture 39 - Sukhatme Test, Consistency of Statistical Tests, Consistency of Mann-Whitney Test
Lecture 40 - General Two Sample Problem, Efficiency of Tests, Hoeffding's U-statistics

References
Statistical Methods for Scientists and Engineers
Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur. This course introduces some important topics in statistical methods used in science and engineering.