# gamma distribution

(40 minutes to learn)

## Summary

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.

## Context

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)

## -Paid-

→ 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)

## -Paid-

→ Mathematical Statistics and Data Analysis

An undergraduate statistics textbook.

Location:
Section 2.2.2, "The gamma density," pages 53-54

## See also

- 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: The 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 .