probability-rs

A small, dependency-free Rust library for probability distributions focused on numerical clarity, clean APIs, and reproducible random sampling.

Current scope:

• Internal RNGs (non-cryptographic): SplitMix64, Xoroshiro128++, Xoshiro256**, PCG32

• Traits: Distribution, Continuous, Discrete, Moments

• Distributions:

• Continuous: Uniform, Normal, Exponential, Lognormal, Gamma, Beta, Chi-squared

• Discrete: Bernoulli, Poisson, Geometric, Binomial

Why

• No external dependencies
• Deterministic sampling (seeded), useful for tests and teaching
• Simple and explicit math with careful domains and parameter checks

Status

This is a work-in-progress library. APIs may evolve. Contributions and feedback are welcome.

Transparency: AI-assisted development

This crate is developed with assistance from large language models (LLMs) to speed up code and documentation drafts. All AI-assisted changes are:

• reviewed by maintainers (human code review);
• validated by tests and checks (cargo test, clippy, CI);
• numerically verified against references when applicable.

API decisions, formulas, and algorithms are confirmed by the maintainers. We do not incorporate third-party content without proper licensing and we do not accept uncurated automated contributions. If you have any concerns about provenance or quality, please open an issue.

Quick start

Add to your workspace as a path dependency or use locally:

# Cargo.toml
[dependencies]
probability-rs = { path = "./probability-rs" }

Example: sampling and basic queries

use probability_rs::dist::{normal, uniform, exponential, bernoulli, poisson, Distribution, Continuous, Discrete, Moments};
use probability_rs::rng::SplitMix64;

fn main() {
let normal = normal::Normal::new(0.0, 1.0).unwrap();
let uniform = uniform::Uniform::new(-1.0, 1.0).unwrap();
let expo = exponential::Exponential::new(2.0).unwrap();
let bern = bernoulli::Bernoulli::new(0.4).unwrap();
let pois = poisson::Poisson::new(3.0).unwrap();

let mut rng = SplitMix64::seed_from_u64(2024);
let x_n = normal.sample(&mut rng);
let x_u = uniform.sample(&mut rng);
let x_e = expo.sample(&mut rng);
let x_b = bern.sample(&mut rng);
let x_p = pois.sample(&mut rng);

println!("Normal sample: {x_n:.6} pdf(0)={:.6}", normal.pdf(0.0));
println!("Uniform sample: {x_u:.6} mean={:.3} var={:.3}", uniform.mean(), uniform.variance());
println!("Exponential sample: {x_e:.6} CDF(1)={:.6}", expo.cdf(1.0));
println!("Bernoulli sample: {x_b} p=0.4 var={:.3}", bern.variance());
println!("Poisson sample: {x_p} lambda=3 pmf(3)={:.6}", pois.pmf(3));
}

Run tests:

cargo test --all

API at a glance

• Distribution (common):

• cdf(x) -> f64, in_support(x) -> bool, sample(&mut Rng) -> Value

• Continuous (f64): pdf(x) -> f64, inv_cdf(p) -> f64

• Discrete (i64): pmf(k) -> f64, inv_cdf(p) -> i64

• Moments: mean() -> f64, variance() -> f64, skewness() -> f64, kurtosis() -> f64 (excess), kurtosis_full() -> f64

• RNG: rng::RngCore, rng::SplitMix64

RNGs: picking the right generator

This crate ships a few small, non-cryptographic PRNGs with a common trait rng::RngCore.

SplitMix64

• Best for: seeding other RNGs, quick-and-simple deterministic tests.

• Pros: tiny, very fast, good bit diffusion; great seed expander.

• Cons: not the strongest statistical quality for long streams compared to xoshiro/pcg.

• Use:

• use probability_rs::rng::SplitMix64;

• let mut rng = SplitMix64::seed_from_u64(123);

Xoroshiro128++

• Best for: fast simulations with small memory footprint (128-bit state).

• Pros: excellent speed, good quality in practice for 64-bit outputs.

• Cons: period 2^128−1; for massive parallel use, consider jump/long_jump to split streams.

• Use:

• use probability_rs::rng::Xoroshiro128PlusPlus;

• let mut rng = Xoroshiro128PlusPlus::seed_from_u64(123);

Xoshiro256**

• Best for: general-purpose high-quality streams (256-bit state).

• Pros: period 2^256−1, excellent statistical properties, jump/long_jump available.

• Cons: slightly larger state than Xoroshiro128++.

• Use:

• use probability_rs::rng::xoshiro256::Xoshiro256StarStar;

• let mut rng = Xoshiro256StarStar::seed_from_u64(123);

PCG32 (XSH RR 64/32)

• Best for: small-state RNG with good 32-bit outputs, reproducible parallel streams.

• Pros: configurable streams via from_seed_and_stream(seed, stream); great distribution.

• Cons: 32-bit output per step (we combine two for 64-bit).

• Use:

• use probability_rs::rng::Pcg32;

• let mut rng = Pcg32::seed_from_u64(123);

• or let mut rng = Pcg32::from_seed_and_stream(STATE, STREAM_ID);

Guidelines by scenario:

• Reproducible tests, quick examples: SplitMix64
• High-throughput simulations (low memory): Xoroshiro128++
• High-quality general-purpose streams: Xoshiro256**
• Many independent parallel streams with small state: PCG32 (use different stream)

Note: none of these RNGs are cryptographic. For security-sensitive contexts, use a proper CSPRNG.

Numerical notes

• Normal CDF/quantile use classic approximations (erf and Acklam’s probit). Tolerances in tests reflect expected approximation error.
• Poisson sampling uses a hybrid approach (inversion, mode-based, and quantile-anchored) depending on λ. PTRS may be added later for λ≫1.

Benchmarks

We use Criterion for micro-benchmarks. To run:

cargo bench

The included benchmark compares Poisson sampling for small (λ=2.5) and large (λ=250) regimes.

Roadmap

Distributions and structure

• More distributions
• Truncation and affine transforms (shift/scale) as generic wrappers
• Mixture models (finite mixtures) with EM fitting

Inference and model assessment

• Parameter estimation: MLE/MOM with uncertainty (Fisher information)
• Model selection: AIC/BIC, automated “best fit” among candidates
• Goodness-of-fit tests: Kolmogorov–Smirnov, Anderson–Darling, chi-squared
• Robust statistics and empirical quantiles with confidence intervals

Advanced sampling and performance

• Faster samplers: Ziggurat or Ratio-of-Uniforms (Normal/Exponential), PTRS for Poisson (λ ≫ 1)
• Alias method (Walker/Vose) for arbitrary categorical distributions
• Variance reduction: antithetic variates, control variates, stratification
• Vectorization/batching (std::simd where feasible), allocation-free sample_n and sample_iter

Dependence and multivariate

• Copulas (Gaussian, Student-t) to construct multivariate dependencies
• Multivariate families: Multivariate Normal, Wishart/Inverse-Wishart, Dirichlet

Stochastic processes and simulation

• Poisson processes (homogeneous/inhomogeneous), renewal processes, simple Hawkes
• Brownian motion, Ornstein–Uhlenbeck; SDE discretizations (Euler–Maruyama)
• Time-series generators: AR(1), light ARMA components for simulations

Practical statistics and summaries

• Histograms, KDE, ECDF, descriptive summaries (median, MAD, etc.)
• Streaming quantiles (P² algorithm, optional t-digest via feature flag)
• Distances/divergences: KL, Jensen–Shannon, Wasserstein (1D)

API ergonomics and safety

• logpdf/logpmf/logcdf/logccdf for numerical stability; ccdf for tail work
• Additional moments: entropy, skewness, kurtosis, cumulants
• SeedableRng-style helper trait; domain types (Probability, Positive, Interval)
• Feature flags: serde, no_std (where viable), simd, special-fns

Numerics and special functions

• Special functions: gamma/incomplete gamma, beta/incomplete beta, digamma/trigamma
• Generic numerical inversion for CDFs (bracketing + Newton/Halley) with tolerances
• Tail-accuracy improvements using log1p/expm1 and complemented functions

Tooling and quality

• Expanded benchmarks (Criterion) and lightweight statistical test harness
• CI with lint/test/bench sanity; performance tracking
• Rich documentation with runnable examples and optional notebooks

License

MIT