Exploring the t distribution

Compare Student's t densities and tail probabilities with the normal as the degrees of freedom change.

Uses phit

Inputs

Degrees of freedom Running

Student's t with 3 degrees of freedom has heavier tails than the normal. Every value here comes from the native distribution functions, which are checked against 60-digit references.

use function Phit\{dist_t_pdf_array, dist_t_sf};

dist_t_pdf_array($xs, 3);  // one native call for the whole grid
2 * dist_t_sf(1.96, 3);      // two-sided tail probability

t critical value (95%): 3.1824
Normal critical value: 1.96

Densities

Two-sided tail probabilities

\|x\| >	t	normal
1.645	0.1985	0.1
1.96	0.1449	0.05
2.576	0.0821	0.01
3.291	0.046	9.983e-4

Script: site/vignettes/distributions.php in phpstats/phit@76b22f0.