English

Bounding Standard Gaussian Tail Probabilities

Statistics Theory 2010-12-21 v3 Statistics Theory

Abstract

We review various inequalities for Mills' ratio (1 - \Phi)/\phi, where \phi and \Phi denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds.

Keywords

Cite

@article{arxiv.1012.2063,
  title  = {Bounding Standard Gaussian Tail Probabilities},
  author = {Lutz Duembgen},
  journal= {arXiv preprint arXiv:1012.2063},
  year   = {2010}
}
R2 v1 2026-06-21T16:56:05.434Z