Evaluating the Normal Distribution

By George Marsaglia. 2004

101 citations recorded by the source corpus.

This article provides a little table-free C function that evaluates the normal distribution with absolute error less than 8 x 10 -16 . A small extension provides relative error near the limit available in double precision: 14 to 16 digits, the limits determined mainly by the computer's ability to evaluate exp(-t) for large t. Results are compared with those provided by calls to erf or erfc functions, the best of which compare favorably, others do not, and all appear to be much more complicated than need be to get either absolute accuracy less than 10-15 or relative accuracy to the exp()-limited 14 to 16 digits. Also provided: A short history of the error function erf and its intended use, as well as, in the "browse files" attachment, various erf or erfc versions used for comparison.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/97f37fbf9466fd38125c1cfcdbb2a68ba0db47d4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Luc De Raedt
2. Manfred Jaeger
3. Bernd Gutmann
4. George Marsaglia
5. Gavin E. Crooks

Citations in the corpus

• Extending ProbLog with Continuous Distributions (2010, methodology): “The reason is, that for x = 4 ∈ [0, 10] the query fails but for x = 6 ∈ [0, 10] it succeeds.”
• Ratios of Normal Variables (2006, methodology): “They also include the Phi function from Marsaglia (2004), needed to avoid integrating tail areas of f(t), as well as a procedure for generating a pair of jointly normal variates z, w, given µz, µw, σz, σw and correlation ρ.”