normal-inverse-gaussian

Description

This library implements the cumulative distribution function of the normal inverse Gaussian (NIG) distribution. The code is written in C++ and includes a Python package installable via pip.

C++ Build

Requirements: a C++17 compiler and CMake >= 3.15.

cmake -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build

This produces:

• build/libnig.a — static library to link against from C++ code.
• build/nig_demo — standalone executable.

The public header is code/include/nig.hpp. Link against libnig and include the header to call nig_cdf directly from C++.

Python Package

Requirements: a C++17 compiler, CMake >= 3.15, and pybind11.

pip install .

This builds and installs the nig package. No manual CMake invocation is needed; scikit-build-core handles the compilation transparently.

Usage

Two interfaces are provided.

Wikipedia parametrisation (α, β, μ, δ):

from nig import nig_cdf

nig_cdf(x=2.0, alpha=2.0, beta=-0.4, mu=1.75, delta=2.0)

SciPy-compatible parametrisation — drop-in replacement for scipy.stats.norminvgauss:

from nig import norminvgauss

# unbound call (same signature as scipy.stats.norminvgauss.cdf)
norminvgauss.cdf(x=2.0, a=4.0, b=-0.8, loc=1.75, scale=2.0)

# frozen distribution
dist = norminvgauss(a=4.0, b=-0.8, loc=1.75, scale=2.0)
dist.cdf(2.0)

The relationship between the two parametrisations is a = alpha * delta, b = beta * delta, loc = mu, scale = delta.

Citation

If you use the library, please cite the paper https://arxiv.org/abs/2502.16015:

@article{Navas-Palencia2025NIG,
  title     = {On the computation of the cumulative distribution function of the Normal
Inverse Gaussian distribution},
  author    = {Navas-Palencia, G.},
  year      = {2025},
  eprint    = {2502.16015},
  archivePrefix = {arXiv},
  primaryClass = {math.NA},
  volume    = {abs/2502.16015},
  url       = {http://arxiv.org/abs/2502.16015},
}