P(X ≤ x).
Inverse survival: x with P(X > x) = p.
Apply one of the functions to every element of a typed / plain array.
Probability density at x.
Inverse cdf: smallest x with P(X ≤ x) ≥ p.
P(X > x) — use for p-values; accurate where 1 − cdf would cancel.
Probability distributions for statistical tests: normal, Student t, chi-square, F.
Each factory returns a frozen distribution with
pdf,cdf,sf(= 1 − cdf, accurate in the upper tail),ppf(inverse cdf) andisf(inverse sf), plusmean/variance. Everything is built on three special functions —lgamma(Lanczos), the regularized incomplete gamma (series + Lentz continued fraction) and the regularized incomplete beta (Lentz) — so the cdf values agree with scipy to ~1e-14 relative in the body and ~1e-12 deep in the tails. Inverses use Acklam's rational approximation refined by Halley steps (normal) or bracketed bisection followed by Newton polish (t, chi², F).dist.normal().cdf(1.96) // 0.9750021… dist.t(10).ppf(0.975) // 2.2281388… dist.chi2(5).sf(11.07) // p-value 0.0500096… dist.f(3, 10).cdf(3.708) // 0.9499912…