Module fisher_f 

Fisher–Snedecor F-distribution — pdf / cdf / quantile + upper-tail p-value, used by ANOVA and variance-ratio tests. CDF is exact via the regularized incomplete beta I_x(d₁/2, d₂/2) with x = d₁f/(d₁f + d₂).

Functions

cdf

cdf P(X ≤ x) = I_x(d₁/2, d₂/2), x = d₁f/(d₁f + d₂).

pdf

pdf with numerator/denominator dof d1, d2 > 0, x ≥ 0.

quantile

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

upper_p

Upper-tail p-value P(X ≥ f) — the ANOVA / variance-ratio p-value.