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Pàgina inicial > Articles > Articles publicats > Approximating Mills ratio |
Data: | 2014 |
Resum: | 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. |
Ajuts: | 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 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Gaussian law ; Mills ratio ; Error function ; Gaussian Q-function |
Publicat a: | Journal of mathematical analysis and applications, Vol. 420 (2014) , p. 1832-1853, ISSN 1096-0813 |
Postprint 20 p, 371.2 KB |