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A series of inequalities for Mills’ ratio. (Chinese) Zbl 0538.62016

The main result of this paper is the following: For any positive integers \(\ell\), s, t and nonnegative integer k, the sign of the \(\ell th\) order determinant \(|(a_{ij}(x))|_{\ell,s,t,k}\) is \((-1)^{k\ell +(s+t)\ell(\ell -1)/2}\) for any x, where \(a_{ij}(x)\) is the \(k+(i- 1)t+(j-1)s th\) derivative of the Mills’ ratio M(x). Some inequalities involving Mills’ ratio are obtained using the above result.
Reviewer: C.-P.Han

MSC:

62E99 Statistical distribution theory
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