Module distributions 

Probability distributions — the canonical, full-precision pdf / cdf / quantile for the whole engine, built on the shared special functions (special).

This is what makes p-values and confidence intervals honest: hypothesis tests (super::hypothesis) get their tail probabilities from a real Student-t / χ² / F CDF here, not a |t| > 1.96 ⇒ p = 0.05 placeholder, and domain libraries reuse normal instead of copying a local normal_cdf.

Submodules (one distribution each, PROJECT RULE §11): special (erf / incomplete gamma & beta), normal, students_t, chi_squared, fisher_f.

Everything here is scalar f64 special-function evaluation — pointwise, not GPU-amenable (CLAUDE.md §13: the CPU path is the right one; the data-aggregate kernels that feed these, e.g. mean/variance, are the Reduction-class work that routes through ComputePolicy).

Modules

chi_squared

χ² (chi-squared) distribution — pdf / cdf / quantile + upper-tail p-value, used by the goodness-of-fit and independence tests. CDF is exact via the regularized lower incomplete gamma P(k/2, x/2) (super::special::gammp).

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).

multivariate_normal

Multivariate normal distribution (PRML ch 2.3) — log-density, sampling, and MLE for a p-dimensional Gaussian. The covariance inverse / log-determinant and the sampling transform reuse linear_algebra::cholesky (no new solver). This is the foundation of the Bayesian spine (Bayesian linear regression, Gaussian processes, mixture/EM with full covariance).

normal

Normal (Gaussian) distribution — pdf / cdf / quantile, the canonical engine-wide implementation. The CDF is ½·erfc(−z/√2) over the shared super::special::erfc (full precision), and the quantile is Acklam’s rational inverse refined by one Halley step (≈ machine precision). Domain libraries (financial_modeling’s Black–Scholes, etc.) should call these instead of re-deriving a local normal_cdf.

special

Special functions underpinning the probability distributions — the canonical, full-double-precision implementations the whole engine shares.

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

beta_pdf

Basic Beta PDF (alpha, beta >0) on (0,1).

binomial_cdf

Binomial CDF via direct sum (small n only; for large use normal approx in caller).

binomial_pmf

Binomial PMF: P(K = k | n, p).

empirical_cdf

Empirical CDF from sorted samples (for caller-sorted data).

exponential_cdf

Exponential CDF.

exponential_pdf

Exponential PDF (rate > 0).

gamma_pdf

Gamma PDF (shape k>0, scale theta>0).

laplace_cdf

Laplace CDF.

laplace_pdf

Laplace (double exponential) PDF.

lognormal_cdf

Lognormal CDF via normal cdf of ln(x).

lognormal_pdf

Lognormal PDF (mu, sigma>0).

poisson_cdf

Poisson CDF.

poisson_pmf

Poisson PMF.

uniform_cdf

Uniform CDF.

uniform_pdf

Uniform PDF on [a, b].

weibull_pdf

Weibull PDF (shape k>0, scale lambda>0).