Evaluation of the Gauss Integral

Dmitri Martila and Stefan Groote
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Dmitri Martila: Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
Stefan Groote: Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia

Stats, 2022, vol. 5, issue 2, 1-8

Abstract: The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler–Poisson) integral over a finite boundary, as is necessary, for instance, for the error function or the cumulative distribution of the normal distribution, cannot be expressed by analytic functions. This is proven by the Risch algorithm. Regardless, there are proposals for approximate solutions. In this paper, we give a new solution in terms of normal distributions by applying a geometric procedure iteratively to the problem.

Keywords: Gauss distribution; normal distribution; error function; approximations (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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