Bounding Standard Gaussian Tail Probabilities

2010/12/09 by Lutz Duembgen, Duembgen, Lutz
Mathematics · Physics and Astronomy · #62E17 #Advanced Mathematical Identities #FOS: Mathematics #Probability and Statistical Research #Statistical Mechanics and Entropy #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1012.2063

openalex publication_date 2010/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review various inequalities for Mills' ratio (1 - Φ)/ϕ, where ϕand Φdenote 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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