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Statistical Methods for Scientists and Engineers. Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur.
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English
English [CC]
FREE
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Description
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 content
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- 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
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- 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
Instructor
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