Log-Quadratic Bounds for the Gaussian Q-function

2013/04/09 by Andrew Mastin, Mastin, Andrew, Patrick Jaillet +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #Random Matrices and Applications #math.PR

paper · pdf · doi:10.48550/arxiv.1304.2488

arxiv created 2013/04/09 · openalex publication_date 2013/04/09 · arxiv updated 2013/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present bounds of quadratic form for the logarithm of the Gaussian Q-function. We also show an analytical method for deriving log-quadratic approximations of the Q-function and give an approximation with absolute error less than 10^-3.

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

Related

• A Chernoff-type Lower Bound for the Gaussian Q-function
• Tight Approximations for the Two Dimensional Gaussian Q-function
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• Two theorems on distribution of Gaussian quadratic forms
• The q-Laplace Transforms compared: the basic confluent hypergeometric function ₂ϕ₀