Mills’ ratio: Monotonicity patterns and functional inequalities ✩

In this paper we study the monotonicity properties of some functions involving the Mills’ ratio of the standard normal law. From these we deduce some new functional inequalities involving the Mills’ ratio, and we show that the Mills’ ratio is strictly completely monotonic. At the end of this paper we present some Turán-type inequalities for Mills’ ratio. © 2007 Elsevier Inc. All rights reserved