(35 minutes to learn)
The student-t distribution is a continuous probability distribution motivated by estimating the mean of a Gaussian population with unknown variance.
This concept has the prerequisites:
- Understand how the student-t distribution is defined in terms of samples drawn from a normal distribution.
- Know how the shape of the distribution depends on the degrees of freedom (few degrees of freedom gives a heavy-tailed distribution, many degrees of freedom means approximately normal)
Core resources (read/watch one of the following)
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: Section 8.4, "The t distributions," pages 480-484
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location: Section 6.2, "Chi-squared, t, and F distributions," pages 192-194
- The student-t distribution is the predictive distribution for Bayesian parameter estimation of Gaussian distributions with unknown variance .
- The distribution is related to the t-test from frequentist statistics.
- This is an example of a heavy-tailed distribution .
- In the multivariate case, the t-distribution can be generalized to Gaussian scale mixtures .