Approximating Mills ratio
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Utzet i Civit, Frederic (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2014
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.
Grants:	Ministerio de Economía y Competitividad MTM2012-33937 Ministerio de Economía y Competitividad MTM2009-08869 Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Gaussian law ; Mills ratio ; Error function ; Gaussian Q-function
Published in:	Journal of mathematical analysis and applications, Vol. 420 (2014) , p. 1832-1853, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2014.05.034

Postprint 20 p, 371.2 KB

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