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Last updated:

September 23, 2023

Duration:

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FREE

This course includes:

Unlimited Duration

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Description

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)

Course Curriculum

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

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