Exponential Family

Explore the comprehensive tutorial on the Exponential Family of probability distributions, covering a wide range of topics from basic concepts to advanced applications. Learn about the mean and variance of exponential families, and delve into specific distributions such as Normal, Bernoulli, Binomial, Poisson, Negative Binomial, Exponential, Pareto, Weibull, Laplace, Chi-square, Gamma, Log Normal, Beta, Multinomial, Inverse Gamma, and Skew-Logistic. Gain practical skills by using R to simulate and confirm theoretical results, and understand the distribution of sufficient statistics. Discover the application of exponential families in multiple linear regression and explore the Cramer-Rao Lower Bound. This in-depth tutorial provides a solid foundation for understanding and working with exponential families in statistical analysis and modeling.

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.