Module mathfn 

Special functions and probability distributions implemented from scratch.

The implementation follows the standard series and continued-fraction methods for the regularized incomplete gamma and beta functions (Numerical Recipes style, with explicit iteration bounds and a structured NonConvergence error). No statrs or platform erf is used; on wasm32 every transcendental falls back to libm.

Functions

abs

beta_cdf

beta_pdf

beta_quantile

beta_sf

Upper tail P(X > x), computed from the mirrored regularized incomplete beta function rather than 1 - cdf.

binomial_cdf

binomial_pmf

chi_square_cdf

chi_square_pdf

chi_square_quantile

chi_square_sf

erf

Error function, computed from the regularized incomplete gamma: erf(x) = P(1/2, x^2) for x >= 0.

erfc

Complementary error function, computed from the regularized upper incomplete gamma so that the positive tail keeps full relative accuracy.

exp

exponential_cdf

exponential_pdf

exponential_quantile

exponential_sf

Upper tail P(X > x) computed from exp directly so large x keeps relative accuracy (never 1 - cdf).

f_cdf

f_pdf

f_quantile

f_sf

Upper tail P(X > x), computed directly from the regularized incomplete beta function so large x keeps relative accuracy.

gamma_cdf

gamma_p

Regularized lower incomplete gamma P(a, x).

gamma_pdf

gamma_q

Regularized upper incomplete gamma Q(a, x).

gamma_quantile

ibeta

Regularized incomplete beta I_x(a, b).

invert_monotone

Invert a strictly increasing CDF by bracket expansion, bisection, and Newton polishing. The tolerance is relative (1e-15), comfortably inside the documented 1e-12 requirement.

lgamma

Lanczos approximation to ln|Gamma(x)|.

ln

lognormal_cdf

lognormal_pdf

lognormal_quantile

negative_binomial_cdf

negative_binomial_pmf

normal_cdf

normal_pdf

normal_quantile

normal_sf

Upper tail P(X > x), computed with erfc so large positive x keeps relative accuracy (never 1 - cdf).

poisson_cdf

poisson_pmf

sin

sqrt

student_t_cdf

student_t_pdf

student_t_quantile

student_t_sf

uniform_cdf

uniform_pdf

uniform_quantile