inverse_gaussian.cpp File Reference

InverseGaussian(μ, λ) / Wald family implementation: mean μ > 0, shape λ > 0. More...

#include "DistributionCommon.h"
#include <algorithm>
#include <cmath>
#include <memory>
#include <optional>
#include <random>
#include <string>
#include <utility>
#include <vector>

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Namespaces
namespace	provsql

Detailed Description

InverseGaussian(μ, λ) / Wald family implementation: mean μ > 0, shape λ > 0.

The first-passage time of Brownian motion with drift: a positive, right-skewed family widely used for reliability and reaction-time models. Its CDF has a closed form in terms of the standard normal Φ, so \(P(X < c)\) and the numeric quantile are analytic; all raw moments are finite (a finite-sum closed form). Positive scalings map c·IG(μ, λ) = IG(cμ, cλ), and a sum of independent inverse Gaussians that share the ratio λ/μ² folds to a single inverse Gaussian in the simplifier (registered as a closure rule below).

Self-contained family implementation: the class is file-local and reaches the evaluators only through the registrars at the bottom (DistributionRegistry factory + sum-closure rule). No evaluator or parser code changes.

Definition in file inverse_gaussian.cpp.