Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating Mills ratio   Consider the Mills ratio $f(x)=\big(1-\Phi(x)\big)/\phi(x), \, x\ge 0$, where
$\phi$ is the density function of the standard Gaussian law and $\Phi$ its
cumulative distribution.We introduce a general procedure to approximate $f$ on
the whole $[0,\infty)$ 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.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph