On D\"umbgen's exponentially modified Laplace continued fraction for Mill's ratio
Florin Avram
TL;DR
This paper improves bounds on the Mills ratio, a key function related to the Gaussian distribution, by refining a continued fraction approximation originally studied by D"umbgen.
Contribution
The paper presents an improved family of bounds for the Mills ratio using an enhanced continued fraction approach.
Findings
New bounds are tighter than previous ones.
The improved bounds enhance accuracy in Gaussian-related probability calculations.
The method refines D"umbgen's continued fraction approximation.
Abstract
The approximation of the Gaussian cumulative distribution or of the related Mills ratio have a long history starting with Gauss and Laplace and continuing nowadays. Below, we improve an important family of bounds provided recently by D\"umbgen.
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Taxonomy
TopicsMathematics and Applications · Mathematical and Theoretical Analysis · History and Theory of Mathematics