Approximating Mills ratio

Armengol Gasull, Frederic Utzet

Research output: Contribution to journalArticleResearchpeer-review

21 Citations (Scopus)


Consider the Mills ratio f(x) = (1 - Φ(x))/φ(x), x≥ 0, where φ is the density function of the standard Gaussian law and Φ its cumulative distribution. We introduce a general procedure to approximate f on the whole [0, ∞) which allows to prove interesting properties where f is involved. As applications we present a new proof that 1/. f is strictly convex, and we give new sharp bounds of f involving rational functions, functions with square roots or exponential terms. Also Chernoff type bounds for the Gaussian Q-function are studied. © 2014 Elsevier Inc.
Original languageEnglish
Pages (from-to)1832-1853
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Dec 2014


  • Error function
  • Gaussian Q-function
  • Gaussian law
  • Mills ratio


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