New inequalities of Mill's ratio and Its Application to The Inverse Q-function Approximation
Information Theory
2021-06-22 v1 math.IT
Statistics Theory
Statistics Theory
Abstract
In this paper, we investigate the Mill's ratio estimation problem and get two new inequalities. Compared to the well known results obtained by Gordon, they becomes tighter. Furthermore, we also discuss the inverse Q-function approximation problem and present some useful results on the inverse solution. Numerical results confirm the validness of our theoretical analysis. In addition, we also present a conjecture on the bounds of inverse solution on Q-function.
Cite
@article{arxiv.1212.4899,
title = {New inequalities of Mill's ratio and Its Application to The Inverse Q-function Approximation},
author = {Pingyi Fan},
journal= {arXiv preprint arXiv:1212.4899},
year = {2021}
}
Comments
12 pages, 4 figures; Submitted to IEEE Trans. Information Theory Dec. 2012