Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417915 | Journal of Mathematical Analysis and Applications | 2014 | 22 Pages |
Abstract
Consider the Mills ratio f(x)=(1âΦ(x))/Ï(x), xâ¥0, where Ï 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,â) 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Armengol Gasull, Frederic Utzet,