Capability: statistical-distributions

Requirements

REQ-DIST-001: All distribution functions live in @suaveplan/random under src/distributions/.

REQ-DIST-010: Exports normal(mu?: number, sigma?: number, rng?: Rng): () => number — Gaussian via Box-Muller. Defaults mu=0, sigma=1.
REQ-DIST-011: Exports logNormal(mu?: number, sigma?: number, rng?: Rng): () => number — exp(normal(mu, sigma)).
REQ-DIST-012: Exports exponential(lambda: number, rng?: Rng): () => number. Throws if lambda <= 0.
REQ-DIST-013: Exports gamma(k: number, theta?: number, rng?: Rng): () => number — Marsaglia-Tsang for k≥1, Ahrens-Dieter for k<1. Default theta=1.
REQ-DIST-014: Exports beta(alpha: number, betaParam: number, rng?: Rng): () => number — ratio of two Gamma samples.
REQ-DIST-015: Exports pareto(alpha: number, rng?: Rng): () => number. Throws if alpha <= 0.
REQ-DIST-016: Exports weibull(k: number, a?: number, b?: number, rng?: Rng): () => number. Defaults a=0, b=1.
REQ-DIST-017: Exports cauchy(a?: number, b?: number, rng?: Rng): () => number. Defaults a=0, b=1.
REQ-DIST-018: Exports logistic(a?: number, b?: number, rng?: Rng): () => number. Defaults a=0, b=1.

REQ-DIST-020: Exports bernoulli(p: number, rng?: Rng): () => 0 | 1. Throws if p outside [0, 1].
REQ-DIST-021: Exports geometric(p: number, rng?: Rng): () => number. Throws if p outside (0, 1].
REQ-DIST-022: Exports binomial(n: number, p: number, rng?: Rng): () => number. Throws if n < 0 or p outside [0, 1].
REQ-DIST-023: Exports poisson(lambda: number, rng?: Rng): () => number — Knuth for λ≤30, rejection method above. Throws if lambda <= 0.

REQ-DIST-030: Exports DistributionConfig — discriminated union: { type: 'normal'; mu?: number; sigma?: number } | { type: 'exponential'; lambda: number } | ... (one member per distribution).
REQ-DIST-031: Exports createSampler(config: DistributionConfig, rng?: Rng): () => number — dispatches to the appropriate distribution factory.
REQ-DIST-032: Exports sample(config: DistributionConfig, rng?: Rng): number — one-shot convenience: createSampler(config, rng)().
REQ-DIST-033: DistributionConfig is a plain JSON-serialisable type. rng is always passed externally, never embedded in config.
REQ-DIST-034: createSampler throws RandomError("RANDOM.DISTRIBUTION.UNKNOWN_TYPE") for unrecognised type values (runtime guard for JS consumers without TypeScript).

REQ-DIST-040: fast-check: for each distribution, generate 10k samples and verify mean/variance are within 5% of theoretical values at standard parameters.
REQ-DIST-041: DistributionConfig round-trips through JSON.parse(JSON.stringify(config)) without loss for all distribution types.