Student t Tails and Moment Boundaries
Compare exact small-degree t tails with a normal law and identify when moments stop existing.
Free theory articleCompare exact small-degree t tails with a normal law and identify when moments stop existing.
Concept & interpretation
The Student t distribution arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. This module explores its exact tails and moments for small degrees of freedom.
Experiment
We can observe the transition of moment existence and behavior of exact tail values by changing the degrees of freedom in the control panel.
- Set Degrees of freedom to 1. Observe that mean and variance do not exist (Cauchy distribution).
- Change Degrees of freedom to 2. The mean exists (0) but variance is infinite.
- Change Degrees of freedom to 4. Mean is 0, variance is 2. Compare the two-sided tail against the normal distribution tail.