Approximating Mills ratio

2013/07/12 by Gasull, Armengol, Utzet, Frederic · 6 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1307.3433

Abstract

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.

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