AdditionalDistributions.jl

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AdditionalDistributions.jl extends the Distributions.jl ecosystem by providing additional discrete, continuous, and multivariate probability distributions that are not yet available in the base package.

It maintains full API compatibility (pdf, cdf, rand, etc.) and emphasizes accuracy, efficiency, and completeness — integrating advanced cumulative probability algorithms for multivariate Gaussian and Student’s t models.

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🔹 Key Features

• 📈 Extensive library of distributions — zero-inflated, generalized, and heavy-tailed families.
• ⚡ High-performance QMC algorithms for multivariate CDFs (MvGaussian, MvTStudent),
  significantly faster than MvNormalCDF.jl with minimal loss in absolute precision (typically within 1e-5–1e-6).
• 🧮 Full API compatibility with Distributions.jl.
• 🧩 Research-oriented architecture, extensible to new distributional forms.
• 🧠 Reproducibility-focused testing, with benchmarks aligned with mvtnorm (R, Genz & Bretz 2002).

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🚀 Example

using AdditionalDistributions

# Univariate and multivariate distributions
d1 = Lomax(α=2.0, λ=3.0)
d2 = ZINB(r=4, θ=0.7, p=0.2)

pdf(d1, 1.5), cdf(d2, 3)

# Accurate CDF for a multivariate t distribution
Σ = [1.0 0.5; 0.5 1.0]
d3 = MvTStudent(ν=5, Σ)
cdf(d3, [-1.0, -1.0], [1.0, 1.0])

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🧩 Performance Highlights

Algorithm	Library	Mean Error	Relative Speed
QMC–Sobol (this package)	AdditionalDistributions.jl	≈ 1e-5	1.5×–3× faster
Adaptive Genz–Bretz	MvNormalCDF.jl	≈ 1e-6	slower
QRSVN (R mvtnorm)	Reference	≈ 1e-6	—

Our implementation sacrifices a marginal amount of absolute precision for a substantial speedup in moderate to high dimensions (3–25).

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🧭 Roadmap

• Add Generalized Hyperbolic and Skew-t families.
• Implement flexible parameter fitting (fit_mle, fit_map).
• Integrate symbolic representations for documentation.
• Parallelize with threads
• Maybe GPU-parallelized QMC backend (planned).

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🤝 Contributing

We welcome contributions! All code follows the design and testing conventions of Distributions.jl, ensuring consistency and interoperability.

Guidelines

• Open an issue to discuss bugs or ideas.
• Use @testitem-based testsets (same as Distributions.jl).
• Follow Documenter.jl docstring style and type annotations.

Pull requests improving:

• distribution coverage,
• algorithmic efficiency,
• or documentation clarity are particularly encouraged.

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Author: Santiago Jiménez License: MIT Repository: Santymax98/AdditionalDistributions.jl