• Corpus ID: 248571862

# Improvements of Polya Upper Bound for Cumulative Standard Normal Distribution and Related Functions

@inproceedings{Eidous2022ImprovementsOP,
title={Improvements of Polya Upper Bound for Cumulative Standard Normal Distribution and Related Functions},
author={Omar M. Eidous},
year={2022}
}
Although there is an extensive literature on the upper bound for cumulative standard normal distribution Φ(𝑥) , there are relatively not sharp for all values of the interested argument 𝑥 . The aim of this paper is to establish a sharp upper bound for Φ(𝑥) , in the sense that its maximum absolute difference from Φ(𝑥) is less than 5.785 × 10 −5 for all values of 𝑥 ≥ 0 . The established bound improves the well-known Polya upper bound and it can be used as an approximation for Φ(𝑥) itself…

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