Module students_t 

Student’s t-distribution — pdf / cdf / quantile + the two-sided p-value the t-tests use. The CDF is exact via the regularized incomplete beta (super::special::betai); the quantile inverts it numerically.

Functions

cdf

cdf P(T ≤ t) with nu degrees of freedom. Uses I_x(ν/2, ½) with x = ν/(ν+t²) and the sign of t.

pdf

pdf of the t-distribution with nu > 0 degrees of freedom.

quantile

Inverse cdf (quantile) for 0 < p < 1.

two_sided_p

Two-sided p-value for a t statistic: 2·(1 − P(T ≤ |t|)) = I_x(ν/2, ½).

upper_p

One-sided upper-tail p-value P(T ≥ t).