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YouTube

Approximations

statisticsmatt via YouTube

Overview

This course focuses on teaching various approximation methods in statistics. By the end of the course, learners will be able to understand and apply the Binomial, Poisson, Chi-square, Normal, and Fisher's approximations. They will also learn how to use R and the Delta Method to approximate distributions, calculate confidence intervals, and estimate parameters using different approximation techniques. The course is designed for individuals interested in advanced statistical methods and their applications in data analysis and research.

Syllabus

The Binomial Distribution as an approximation to the Hypergeometric Distribution.
The Poisson Distribution as an approximation to the Binomial Distribution.
Chi square approximation to an F Distribution.
Delta Method (univariate).
Normal Approximation to the t Distribution.
Fisher's Approximation to the square root of a chi-squared distribution.
(1/2) Using R and the Delta Method to Approximate the Distribution of a Function of the Sample Mean.
(2/2) Using R and the Delta Method to Approximate the Distribution of a Function of the Sample Mean.
Asymptotic C I for the Difference of 2 Independent Population Means.
Welch's Approximation to a Confidence Interval for 2 normal population means.
Exact C I for the difference of 2 independent normal population means.
1st 4 moments of the sample mean when x is a Bernoulli random variable.
Approximate Mean and Variance of a Function of the Sample Mean.
Multivariate Normal Distribution as an approximation to the Multinomial Distribution.
Normal Approximation to the Negative Binomial.
Method of Moments Estimation for a Beta Distribution (part 1).
Prove Pearson's Goodness of Fit Test Statistic limits to a Chi-sq Distribution.

Taught by

statisticsmatt

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