# InfoCoBuild

## 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.