Documentation
¶
Overview ¶
Package statdist holds the distribution primitives shared by the statistical operators: the Student-t tail, CDF, quantile and two-sided critical value, and the regularized incomplete beta they rest on.
It is a LEAF (stdlib only today; gonum is allowed) so both internal/processing (TEST_* operators, overlays) and internal/processing/regression (REG_* coefficient p-values, Bayes credible intervals) import one implementation without a cycle. TestStatdistImportBoundary enforces the ceiling.
Every primitive is checked against R to a relative 1e-10 by reference_oracle_test.go (goldens under internal/processing/testdata/reference/, regenerated with `make reference`).
Bit-identity note: the helpers keep their function boundaries (studentTBetaArgs, regularizedIncompleteBetaLog, logBeta, LgammaCorrection, betacf, newtonBracketed) on purpose. Go may fuse a*b+c into an FMA differently on arm64 once an operand is folded in across a boundary, so restructuring them can move results by an ulp.
Index ¶
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
func LgammaCorrection ¶
LgammaCorrection returns the Stirling remainder
δ(x) = lgamma(x) − ((x − ½)·log x − x + log √(2π))
for x ≥ 10 via its asymptotic series Σ B₂ₙ / (2n(2n−1) x^{2n−1}). Eight terms leave a truncation error below 1e-15 at x = 10. Exported for processing's incomplete-gamma prefactor (chi-square).
func RegularizedIncompleteBetaXY ¶
RegularizedIncompleteBetaXY returns I_x(a, b) given x and y = 1 - x computed independently by the caller. Uses the continued-fraction expansion from Numerical Recipes (3rd ed.) Section 6.4, with the prefactor x^a y^b / B(a, b) assembled in log space from logBeta (Stirling-corrected, so no lgamma cancellation at large a or b).
func StudentTCDF ¶
StudentTCDF returns P(T ≤ t) for T ~ t(df). Built on the same incomplete-beta identity as StudentTTwoSidedP — symmetry around zero pins the t < 0 branch.
func StudentTInverseTwoSided ¶
StudentTInverseTwoSided returns the q > 0 with P(|T| ≥ q) = alpha for df degrees of freedom — the two-sided critical value used for confidence-interval bounds.
Solved on log(p) by a bracketed Newton iteration (bisection fallback) on StudentTTwoSidedP, so the root is as accurate as the p-value itself in every tail — including df = 1, where q ≈ 2/(π·alpha) is far past any fixed search bracket. Returns NaN on degenerate inputs (df ≤ 0, alpha outside (0, 1), NaN).
func StudentTQuantile ¶
StudentTQuantile returns the inverse Student-t CDF at probability p: the t* with P(T ≤ t*) = p for T ~ t(df). By symmetry t* is ∓ the two-sided critical value at alpha = 2·min(p, 1−p) (1−p is exact for p ≥ ½).
Degenerate inputs: NaN p or df, or df ≤ 0 → NaN; p ≤ 0 → −Inf; p ≥ 1 → +Inf; p = 0.5 → 0 exactly.
func StudentTTwoSidedP ¶
StudentTTwoSidedP returns the two-sided p-value of a Student's t statistic with df degrees of freedom: P(|T| ≥ |t|).
Derivation: the survival function of |T| equals the regularized incomplete beta I_x(df/2, 1/2) evaluated at x = df / (df + t²). Both x and its complement y = t² / (df + t²) are formed directly (never y = 1 - x), so a tiny t at large df keeps full precision.
Returns NaN for df ≤ 0 or a NaN input, 0 for |t| = ∞ and 1 for t = 0.
Types ¶
This section is empty.
Source Files