A Chernoff-type Lower Bound for the Gaussian Q-function

2012/02/29 by François D. Côté, F. Cote, Ioannis Psaromiligkos +5 · 1 citation
Engineering · Mathematics · #60E15 #FOS: Mathematics #Mathematical Analysis and Transform Methods #Probability (math.PR) #Random Matrices and Applications #Sparse and Compressive Sensing Techniques #math.PR #msc:60E15

paper · pdf · doi:10.48550/arxiv.1202.6483

3 pages. This version replaces the bound in v1 with a tighter bound. We give a proof of the tighter bound and defer the discussion

openalex publication_date 2012/02/29 · arxiv created 2012/03/22 · arxiv updated 2012/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

A lower bound for the Gaussian Q-function is presented in the form of a single exponential function with parametric order and weight. We prove the lower bound by introducing two functions, one related to the Q-function and the other similarly related to the exponential function, and by obtaining inequalities that indicate the sign of the difference of the two functions.

Citations

• Values of Mills' Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument
• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations

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