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Exponential Family

statisticsmatt via YouTube

Overview

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This course covers the Exponential Family, including various distributions and their properties. By the end of the course, learners will be able to understand the mean and variance of different distributions, simulate theoretical results using R, perform multiple linear regression, and analyze the Cramer-Rao Lower Bound. The course teaches skills such as using R for simulation and confirmation, understanding sufficient statistics, and applying different distributions in statistical analysis. The teaching method involves theoretical explanations, practical simulations using R, and application-based examples. This course is intended for individuals interested in advanced statistics, data analysis, and modeling.

Syllabus

Exponential Family: Mean and Variance.
Exponential Family: Normal Distribution.
Exponential Family: Bernoulli Distribution.
Exponential Family: Binomial Distribution (fixed n).
Exponential Family: Poisson Distribution.
Exponential Family: Negative Binomial Distribution (fixed r).
Exponential Family: Exponential Distribution.
Exponential Family: Pareto Distribution (known minimum).
Exponential Family: Weibull Distribution (known k).
Exponential Family: Laplace Distribution (known mean).
Exponential Family: Chi square Distribution.
Exponential Family: Gamma Distribution.
Exponential Family: Log Normal Distribution.
Exponential Family: Beta Distribution.
Exponential Family: Multinomial Distribution (fixed n).
Exponential Family: Using R to simulate and confirm the theoretical results.
Exponential Family: Inverse Gamma.
Using R to confirm the moments of sufficient statistics of an inverse gamma distribution.
Exponential Family: Multiple Linear Regression.
Distribution of a sufficient statistics from a 1-parameter exponential family.
Exponential Family: Skew-Logistic Distribution.
Exponential Family: Cramer-Rao Lower Bound.

Taught by

statisticsmatt

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