beta distribution
(55 minutes to learn)
Summary
The beta distribution is a probability distribution over the unit interval. It is most commonly used in Bayesian statistics as the conjugate prior for the Bernoulli distribution.
Context
This concept has the prerequisites:
- random variables
- expectation and variance
- gamma function (The gamma function is part of the normalizing constant of the beta distribution.)
Goals
- Know the PDF of the beta distribution
- Be able to compute the expectation of a beta random variable
- Express the uniform distribution as a special case of the beta distribution
Core resources (read/watch one of the following)
-Paid-
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location:
Section 5.10, "The beta distribution," pages 303-308
Additional dependencies:
- binomial distribution
Other notes:
- The proof of the identity about products of gamma functions is optional.
Supplemental resources (the following are optional, but you may find them useful)
-Paid-
→ A First Course in Probability
An introductory probability textbook.
Location:
Section 5.6.4, "The beta distribution," pages 240-241
See also
- The beta distribution is the conjugate prior for the Bernoulli and binomial distributions.
- The Dirichlet distribution is a multivariate generalization of the beta distribution.