Recursive Numerical Evaluation of the Cumulative Bivariate Normal Distribution

TL;DR

This paper introduces a recursive algorithm for efficiently computing the cumulative bivariate normal distribution, extending univariate methods with mathematical transparency and adaptability to arbitrary precision.

Contribution

The paper presents a novel recursive algorithm for the bivariate normal distribution, building on Marsaglia's univariate approach, with improved performance and extendability.

Findings

Algorithm is mathematically transparent.

Delivers competitive computational performance.

Easily extendable to arbitrary precision.

Abstract

We propose an algorithm for evaluation of the cumulative bivariate normal distribution, building upon Marsaglia's ideas for evaluation of the cumulative univariate normal distribution. The algorithm is mathematically transparent, delivers competitive performance and can easily be extended to arbitrary precision.