Mills' ratio: Reciprocal convexity and functional inequalities

Details Mills' ratio: Reciprocal convexity and functional inequalities Mills' ratio: Reciprocal convexity and functional inequalities

2010-10-15

arxiv.org/abs/1010.3267v3

Mathematics

Classical Analysis and ODEs

Scientific paper

This note contains sufficient conditions for the probability density function
of an arbitrary continuous univariate distribution, supported on $(0,\infty),$
such that the corresponding Mills ratio to be reciprocally convex (concave). To
illustrate the applications of the main results, the reciprocal convexity
(concavity) of Mills ratio of the gamma distribution is discussed in details.

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