Bounding Standard Gaussian Tail Probabilities

By L. Duembgen. 2010

55 citations recorded by the source corpus.

We review various inequalities for Mills' ratio (1 - Φ)= O, where O and Φ 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.

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1. Nolan Shah
2. Armengol Gasull
3. Weidong Larry Shi
4. Lei Xu
5. Lin Chen
6. Yang Lu
7. Frederic Utzet
8. Zhimin Gao

Citations in the corpus

• On Security Analysis of Proof-of-Elapsed-Time (PoET) (2017, background): “There are various improved bounds and we refer the reader to a nice technical report [10] which gives a survey.”
• Approximating Mills ratio (2013, background): “4 More bounds with rational or exponential functions The topic of searching new bounds for the Mills ratio seems inexhaustible, and we would like to mention the papers of Dümbgen [12] and Avram [2] where new methodologies are presented.”