On the computation of the cumulative distribution function of the Normal Inverse Gaussian distribution

TL;DR

This paper introduces new series and asymptotic expansions for the normal inverse Gaussian CDF, significantly improving computational speed and accuracy over existing numerical methods through a detailed C++ implementation.

Contribution

It presents novel series and asymptotic expansions for the NIG CDF, enhancing computational efficiency and accuracy with a thoroughly tested C++ algorithm.

Findings

Speed-ups of 5 to 60 times over existing methods

Enhanced accuracy in CDF computation

Validated performance through extensive benchmarking

Abstract

In this paper, we obtain various series and asymptotic expansions involving the modified Bessel function of the second kind for the normal inverse Gaussian cumulative distribution function. The new expansions accelerate computations, complementing the numerical integration methods implemented in statistical software packages. We also provide a detailed description of the algorithm and its corresponding implementation in C++. The performance and accuracy of the algorithm are extensively tested and benchmarked with open-source implementations, offering superior accuracy and speed-ups of a factor from 5 to 60.