(40 minutes to learn)
The gamma distribution is a continuous distribution which gives the waiting time for n events to occur, when each event is equally likely to happen at any point in time. It is also commonly used in Bayesian statistics as a prior for scale variables.
This concept has the prerequisites:
- gamma function (The gamma function is needed to define the gamma distribution.)
- random variables
- expectation and variance
Core resources (read/watch one of the following)
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: Section 5.9, "The gamma distribution," pages 295-301
→ A First Course in Probability
An introductory probability textbook.
Location: Section 5.6.1, "The gamma distribution," pages 237-239
Supplemental resources (the following are optional, but you may find them useful)
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location: Section 2.2.2, "The gamma density," pages 53-54
- The gamma distribution is used to construct a prior for the scale parameters in Bayesian parameter estimation.
- The gamma distribution is a member of the exponential family .
- The Wishart distribution is a generalization of the gamma distribution to positive semidefinite matrices.
- Some special cases of the gamma distribution:student-t distribution is a heavy-tailed distribution constructed from the Gaussian distribution and gamma distribution.
- Gamma distributions are used to model the intervals between neuronal firings .
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